Discovering governing equations from data: Sparse identification of nonlinear dynamical systems

Abstract

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technological achievements, including aircraft, combustion engines, satellites, and electrical power. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing physical equations from measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized, time-varying, or externally forced systems.

26 Pages, 13 Figures, 7 Tables

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• Using machine learning to compress the matter transfer function $T(k)$
• Variational Autoencoders for Learning Nonlinear Dynamics of Physical Systems
• Sparse Convolution-based Markov Models for Nonlinear Fluid Flows
• PGD-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit
• Data-driven discovery of multiscale chemical reactions governed by the law of mass action
• Hard Encoding of Physics for Learning Spatiotemporal Dynamics
• Entropic Causal Inference for Neurological Applications
• Learning-informed parameter identification in nonlinear time-dependent PDEs
• Globally Optimal Symbolic Regression
• Calibration of projection-based reduced-order models for unsteady compressible flows
• Learning Discrepancy Models From Experimental Data
• Automated Learning of Interpretable Models with Quantified Uncertainty
• Learning orbital dynamics of binary black hole systems from gravitational wave measurements
• System Identification Through Lipschitz Regularized Deep Neural Networks
• Information-driven transitions in projections of underdamped dynamics
• Learning dynamical systems from data: A simple cross-validation perspective, part III: Irregularly-Sampled Time Series
• Nonlinear Model Predictive Control of a Robotic Soft Esophagus
• Beyond Navier--Stokes equations: Capillarity of ideal gas
• Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approaches
• Learning Thermodynamically Stable and Galilean Invariant Partial Differential Equations for Non-equilibrium Flows
• Full and Reduced Order Model Consistency of the Nonlinearity Discretization in Incompressible Flows
• Investigating climate tipping points under various emission reduction and carbon capture scenarios with a stochastic climate model
• Reduced Order Modeling with Shallow Recurrent Decoder Networks
• On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation
• Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
• Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics
• Ogden Material Calibration via Magnetic Resonance Cartography, Parameter Sensitivity, and Variational System Identification
• Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants
• Data-driven model reduction of agent-based systems using the Koopman generator
• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• Physics-agnostic and Physics-infused machine learning for thin films flows: modeling, and predictions from small data
• A Unified Framework for Sparse Relaxed Regularized Regression: SR3
• Data-Driven Statistical Reduced-Order Modeling and Quantification of Polycrystal Mechanics Leading to Porosity-Based Ductile Damage
• CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting
• GoRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws
• Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equations
• Locally linear embedding for transient cylinder wakes
• Tensor network approaches for learning non-linear dynamical laws
• Data-driven Discovery of Partial Differential Equations for Multiple-Physics Electromagnetic Problem
• Differentiable Physics: A Position Piece
• TorchSISSO: A PyTorch-Based Implementation of the Sure Independence Screening and Sparsifying Operator for Efficient and Interpretable Model Discovery
• Data-driven Discovery of Delay Differential Equations with Discrete Delays
• CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation
• A Safe Reinforcement Learning Algorithm for Supervisory Control of Power Plants
• On the data-driven description of lattice materials mechanics
• Data-Driven Optimal Control of Tethered Space Robot Deployment with Learning Based Koopman Operator
• Structural Inference of Networked Dynamical Systems with Universal Differential Equations
• Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning
• PDE-Driven Spatiotemporal Disentanglement
• Extracting Non-Gaussian Governing Laws from Data on Mean Exit Time
• On the Convergence of the SINDy Algorithm
• Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations
• Model Structural Inference using Local Dynamic Operators
• Combining data assimilation and machine learning to infer unresolved scale parametrisation
• A practical method for estimating coupling functions in complex dynamical systems
• Adaptive Koopman Embedding for Robust Control of Complex Nonlinear Dynamical Systems
• Identifying nonlinear dynamical systems with multiple time scales and long-range dependencies
• Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models
• CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation
• tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format
• Inverse multiobjective optimization: Inferring decision criteria from data
• Data-driven discovery of a heat flux closure for electrostatic plasma phenomena
• A one-dimensional flow model enhanced by machine learning for simulation of vocal fold vibration
• Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition
• Black and Gray Box Learning of Amplitude Equations: Application to Phase Field Systems
• Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models
• Data-driven reduced-order modeling for nonautonomous dynamical systems in multiscale media
• Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction
• Distributed computing for physics-based data-driven reduced modeling at scale: Application to a rotating detonation rocket engine
• Predictive Accuracy of Dynamic Mode Decomposition
• Learning Generalized Quasi-Geostrophic Models Using Deep Neural Numerical Models
• Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents
• Data-Driven Models for Control Engineering Applications Using the Koopman Operator
• Bridging the Gap: Machine Learning to Resolve Improperly Modeled Dynamics
• Kernel Methods for the Approximation of the Eigenfunctions of the Koopman Operator
• Data-driven reduced order models using invariant foliations, manifolds and autoencoders
• Hamiltonian Neural Networks with Automatic Symmetry Detection
• Computational model discovery with reinforcement learning
• A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings
• Motor State Prediction and Friction Compensation for Brushless DC Motor Drives Using Data-Driven Techniques
• Machine learning unveils the linear matter power spectrum of modified gravity
• Machine Discovery of Partial Differential Equations from Spatiotemporal Data
• Sparse Symplectically Integrated Neural Networks
• SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning
• Discovery of Dynamics Using Linear Multistep Methods
• On the sample complexity of stabilizing linear dynamical systems from data
• Random Feature Models for Learning Interacting Dynamical Systems
• Estimating covariant Lyapunov vectors from data
• Autonomous learning of nonlocal stochastic neuron dynamics
• Influence of initial conditions on data-driven model identification and information entropy for ideal mhd problems
• Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
• Learning Dynamics from Multicellular Graphs with Deep Neural Networks
• Extracting structured dynamical systems using sparse optimization with very few samples
• Identifiability Implies Robust, Globally Exponentially Convergent On-line Parameter Estimation: Application to Model Reference Adaptive Control
• Manifold Learning for Organizing Unstructured Sets of Process Observations
• Data-Driven Filtered Reduced Order Modeling Of Fluid Flows
• Metalearning generalizable dynamics from trajectories
• Designing two-dimensional limit-cycle oscillators with prescribed trajectories and phase-response characteristics
• Non-intrusive reduced-order modeling for dynamical systems with spatially localized features
• SubTSBR to tackle high noise and outliers for data-driven discovery of differential equations
• Efficient time stepping for numerical integration using reinforcement learning
• Control Pneumatic Soft Bending Actuator with Feedforward Hysteresis Compensation by Pneumatic Physical Reservoir Computing
• Bridging Scales: a Hybrid Model to Simulate Vascular Tumor Growth and Treatment Response
• On the Universal Transformation of Data-Driven Models to Control Systems
• Bayesian Modelling of Pattern Formation from One Snapshot of Pattern
• Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery
• Physics-informed active learning with simultaneous weak-form latent space dynamics identification
• A Spectral Approach for Learning Spatiotemporal Neural Differential Equations
• Entangled gene regulatory networks with cooperative expression endow robust adaptive responses to unforeseen environmental changes
• Flow control by a hybrid use of machine learning and control theory
• Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures
• Deep Learning Convective Flow Using Conditional Generative Adversarial Networks
• Learning the Tangent Space of Dynamical Instabilities from Data
• Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data
• Data-driven discovery of stochastic dynamical equations of collective motion
• Learning chemical reaction networks from trajectory data
• Learning Differential Operators for Interpretable Time Series Modeling
• CINDy: Conditional gradient-based Identification of Non-linear Dynamics -- Noise-robust recovery
• Identification of Forced Oscillation Sources in Wind Farms using E-SINDy
• Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming
• Data-driven modeling and parameter estimation of Nonlinear systems
• A Data Driven Method for Computing Quasipotentials
• Modeling Unknown Stochastic Dynamical System via Autoencoder
• Self-tuning model predictive control for wake flows
• Machine Learning for Robust Identification of Complex Nonlinear Dynamical Systems: Applications to Earth Systems Modeling
• Data-Driven Modeling of Nonlinear Traveling Waves
• Learning a Reduced Basis of Dynamical Systems using an Autoencoder
• A sparse regression approach to modeling the relation between galaxy stellar masses and their host halos
• Route to Chaos in the Fluidic Pinball
• Codiscovering graphical structure and functional relationships within data: A Gaussian Process framework for connecting the dots
• Feature space approximation for kernel-based supervised learning
• Promoting global stability in data-driven models of quadratic nonlinear dynamics
• Learned SVD: solving inverse problems via hybrid autoencoding
• Analysis of chaotic dynamical systems with autoencoders
• How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning
• Decoupling approximation robustly reconstructs directed dynamical networks
• Learning stochastic dynamical systems with neural networks mimicking the Euler-Maruyama scheme
• Discretization of parameter identification in PDEs using Neural Networks
• Data-assisted, physics-informed propagators for recurrent flows
• Constrained Sparse Galerkin Regression
• Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations
• Schrodinger dynamics and Berry phase of undulatory locomotion
• How more data can hurt: Instability and regularization in next-generation reservoir computing
• Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
• Machine Learning of Partial Differential Equations from Noise Data
• SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics
• Predicting continuum breakdown with deep neural networks
• Dynamical systems and complex networks: A Koopman operator perspective
• Cluster-based control of nonlinear dynamics
• Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint
• Data-driven sparse modeling of oscillations in plasma space propulsion
• Learning the Latent dynamics of Fluid flows from High-Fidelity Numerical Simulations using Parsimonious Diffusion Maps
• Bayesian Learning of Coupled Biogeochemical-Physical Models
• Optimizing Neural Networks via Koopman Operator Theory
• System identification based on characteristic curves: a mathematical connection between power series and Fourier analysis for first-order nonlinear systems
• Forecasting and predicting stochastic agent-based model data with biologically-informed neural networks
• Identification of Physical Processes and Unknown Parameters of 3D Groundwater Contaminant Problems via Theory-guided U-net
• Backpropagation on Dynamical Networks
• The Occupation Kernel Method for Nonlinear System Identification
• Vid2Param: Modelling of Dynamics Parameters from Video
• Influence of Aspect Ratio and Flow Compressibility on Flow Dynamics in a Confined Cavity
• Discovering time-varying aeroelastic models of a long-span suspension bridge from field measurements by sparse identification of nonlinear dynamical systems
• Effects of confinement, impinging shock deflection angle, and Mach number on the flow field of a supersonic open cavity
• Learning dynamics on invariant measures using PDE-constrained optimization
• Modal Analysis of Fluid Flows: An Overview
• Rapidly Encoding Generalizable Dynamics in a Euclidean Symmetric Neural Network
• Reconstructing dynamics of complex systems from noisy time series with hidden variables
• Non-intrusive reduced order models for partitioned fluid-structure interactions
• Effective equations for reaction coordinates in polymer transport
• Projection-based model reduction of dynamical systems using space-time subspace and machine learning
• Hierarchical deep learning-based adaptive time-stepping scheme for multiscale simulations
• Learning ODE Models with Qualitative Structure Using Gaussian Processes
• Early Warning Signals for Bifurcations Embedded in High Dimensions
• Improving the Adaptive Moment Estimation (ADAM) stochastic optimizer through an Implicit-Explicit (IMEX) time-stepping approach
• Hamiltonian Learning using Machine Learning Models Trained with Continuous Measurements
• A divide and conquer method for symbolic regression
• Data-driven learning of non-autonomous systems
• Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
• Memory-based reduced modelling and data-based estimation of opinion spreading
• A deep learning approach to wall-shear stress quantification: From numerical training to zero-shot experimental application
• LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes
• Renormalization Group as a Koopman Operator
• A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations
• Data-Driven Substructuring Technique for Pseudo-Dynamic Hybrid Simulation of Steel Braced Frames
• Data-Driven Modeling of an Unsaturated Bentonite Buffer Model Test Under High Temperatures Using an Enhanced Axisymmetric Reproducing Kernel Particle Method
• Preserving Bifurcations through Moment Closures
• The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation
• The Newton Scheme for Deep Learning
• Robust discovery of partial differential equations in complex situations
• Online Weak-form Sparse Identification of Partial Differential Equations
• Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data
• Linear identification of nonlinear systems: A lifting technique based on the Koopman operator
• An Extensible Benchmark Suite for Learning to Simulate Physical Systems
• Kernel-based parameter estimation of dynamical systems with unknown observation functions
• The structure of global conservation laws in Galerkin plasma models
• Numerical Identification of Nonlocal Potential in Aggregation
• Correlating Time Series with Interpretable Convolutional Kernels
• One-shot learning for solution operators of partial differential equations
• Energy-Preserving Reduced Operator Inference for Efficient Design and Control
• Adaptive parameters identification for nonlinear dynamics using deep permutation invariant networks
• Neural Network Predicts Ion Concentration Profiles under Nanoconfinement
• Improving full-waveform inversion based on sparse regularisation for geophysical data
• Data-Driven Optimal Control Using Perron-Frobenius Operator
• RODE-Net: Learning Ordinary Differential Equations with Randomness from Data
• Stepwise Model Reconstruction of Robotic Manipulator Based on Data-Driven Method
• Artificial neural network approach for turbulence models: A local framework
• Living in the Physics and Machine Learning Interplay for Earth Observation
• Physics-based Machine Learning Discovered Nano-circuitry for Nonlinear Ion Transport in Nanoporous Electrodes
• Evaluating the Stability of Deep Learning Latent Feature Spaces
• Statistical Mechanics of Dynamical System Identification
• Enhancing model identification with SINDy via nullcline reconstruction
• 3D tracking of particles in a dusty plasma by laser sheet tomography
• Data-driven Selection of Coarse-Grained Models of Coupled Oscillators
• Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations
• Green's matching: an efficient approach to parameter estimation in complex dynamic systems
• Network-theoretic modeling of fluid-structure interactions
• Latent assimilation with implicit neural representations for unknown dynamics
• Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
• Data Set Description: Identifying the Physics Behind an Electric Motor -- Data-Driven Learning of the Electrical Behavior (Part II)
• Enhancing Dynamical System Modeling through Interpretable Machine Learning Augmentations: A Case Study in Cathodic Electrophoretic Deposition
• Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics
• Localization of Invariable Sparse Errors in Dynamic Systems
• Discovery of Governing Equations with Recursive Deep Neural Networks
• Vision-based system identification and 3D keypoint discovery using dynamics constraints
• LFT Representation of a Class of Nonlinear Systems: A Data-Driven Approach
• Robust reconstruction of sparse network dynamics
• Video Extrapolation with an Invertible Linear Embedding
• Sparse system identification by low-rank approximation
• Bayesian Dynamical System Identification With Unified Sparsity Priors And Model Uncertainty
• A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs
• A Supervised Machine-Learning Approach For Turboshaft Engine Dynamic Modeling Under Real Flight Conditions
• Learning surrogate equations for the analysis of an agent-based cancer model
• Multi-stage model predictive control for slug flow crystallizers using uncertainty-aware surrogate models
• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
• Sparse identification of multiphase turbulence closures for coupled fluid--particle flows
• Principled interpolation of Green's functions learned from data
• CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations
• Tailored minimal reservoir computing: on the bidirectional connection between nonlinearities in the reservoir and in data
• Context-aware controller inference for stabilizing dynamical systems from scarce data
• Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videos
• Data-driven formulation of natural laws by recursive-LASSO-based symbolic regression
• Manifold Coordinates with Physical Meaning
• Data-driven discovery of mechanical models directly from MRI spectral data
• Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing
• Dynamics of tidal spiral arms: Machine learning-assisted identification of equations and application to the Milky Way
• Statistical Guarantees in Data-Driven Nonlinear Control: Conformal Robustness for Stability and Safety
• A Comparison of Data-Driven Techniques for Power Grid Parameter Estimation
• Learning Partially Known Stochastic Dynamics with Empirical PAC Bayes
• Nonlinear second-order dynamics describe labial constriction trajectories across languages and contexts
• Constrained or Unconstrained? Neural-Network-Based Equation Discovery from Data
• Learning from learning machines: a new generation of AI technology to meet the needs of science
• Using Covariant Lyapunov Vectors to Quantify High Dimensional Chaos with a Conservation Law
• A Model-Constrained Tangent Slope Learning Approach for Dynamical Systems
• Koopman-Based Surrogate Models for Multi-Objective Optimization of Agent-Based Systems
• Extending the trapping theorem to provide local stability guarantees for quadratically nonlinear models
• A non-autonomous equation discovery method for time signal classification
• STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations
• Nonlinear normal modes in the $\beta$-Fermi-Pasta-Ulam-Tsingou chain
• Discovering dynamical laws for speech gestures
• Data-driven observer design for an inertia wheel pendulum with static friction
• ERFit: Entropic Regression Fit Matlab Package, for Data-Driven System Identification of Underlying Dynamic Equations
• Reverse engineering learned optimizers reveals known and novel mechanisms
• A Neural Network Ensemble Approach to System Identification
• Bistable flow dynamics of airfoil stall under varying angle of attack: A stochastic model with multiplicative noise
• Machine Learning in Viscoelastic Fluids via Energy-Based Kernel Embedding
• Data-driven Initial Gap Identification of Piecewise-linear Systems using Sparse Regression and Universal Approximation Theorem
• Data-driven discovery of dynamics from time-resolved coherent scattering
• Time-Resolved Reconstruction of Motion, Force, and Stiffness using Spectro-Dynamic MRI
• Theoretical Foundations for the Dynamic Mode Decomposition of High Order Dynamical Systems
• Data-driven input-to-state stabilization with respect to measurement errors
• Hybrid Scheme of Kinematic Analysis and Lagrangian Koopman Operator Analysis for Short-term Precipitation Forecasting
• Fourier Series-Based Approximation of Time-Varying Parameters in Ordinary Differential Equations
• Sparse identification of quasipotentials via a combined data-driven method
• Assessment of hybrid machine learning models for non-linear system identification of fatigue test rigs
• Stability Preserving Data-driven Models With Latent Dynamics
• Learning Data-Driven PCHD Models for Control Engineering Applications
• Data-Driven Theory-guided Learning of Partial Differential Equations using SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE)
• Time-Reversal Symmetric ODE Network
• Solving physics-based initial value problems with unsupervised machine learning
• Analytical Mechanics Allows Novel Vistas on Mathematical Epidemic Dynamics Modelling
• Data-driven Discovery of Invariant Measures
• Stable Sparse Operator Inference for Nonlinear Structural Dynamics
• Data-Driven Closure of Projection-Based Reduced Order Models for Unsteady Compressible Flows
• Network reconstruction may not mean dynamics prediction
• SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networks
• Dynamic mode decomposition for compressive system identification
• Data-Augmented Predictive Deep Neural Network: Enhancing the extrapolation capabilities of non-intrusive surrogate models
• A sparse regression approach for populating dark matter halos and subhalos with galaxies
• Data-driven model reconstruction for nonlinear wave dynamics
• Learning Hidden Physics and System Parameters with Deep Operator Networks
• CONFIDE: Contextual Finite Differences Modelling of PDEs
• Learning Runge-Kutta Integration Schemes for ODE Simulation and Identification
• Data-driven system identification using quadratic embeddings of nonlinear dynamics
• Boosting on the shoulders of giants in quantum device calibration
• Explicit Estimation of Derivatives from Data and Differential Equations by Gaussian Process Regression
• Systematically designing better instance counting models on cell images with Neural Arithmetic Logic Units
• On data-driven stabilization of systems with quadratic nonlinearities
• Methods to Recover Unknown Processes in Partial Differential Equations Using Data
• Network-based analysis of fluid flows: Progress and outlook
• Milky Way Mapper decoded abundances -- I. Shared disc enrichment patterns
• Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
• From reductionism to realism: Holistic mathematical modelling for complex biological systems
• Learning Interaction Kernels for Agent Systems on Riemannian Manifolds
• Bayesian variable selection in linear dynamical systems
• A General Framework for Linking Free and Forced Fluctuations via Koopmanism
• Physics-informed Spline Learning for Nonlinear Dynamics Discovery
• A quantum inspired approach to learning dynamical laws from data -- block-sparsity and gauge-mediated weight sharing
• Non-intrusive inference reduced order model for fluids using linear multistep neural network
• Exploring Fresnel diffraction at a straight edge with a neural network
• Physics-aware, probabilistic model order reduction with guaranteed stability
• Machine learning and serving of discrete field theories -- when artificial intelligence meets the discrete universe
• SINDy with Control: A Tutorial
• Deep learning of parameterized equations with applications to uncertainty quantification
• Learning emergent PDEs in a learned emergent space
• Electron neural closure for turbulent magnetosheath simulations: energy channels
• Space-Filling Subset Selection for an Electric Battery Model
• Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds
• Assessment of End-to-End and Sequential Data-driven Learning of Fluid Flows
• Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares
• Celestial Machine Learning: From Data to Mars and Beyond with AI Feynman
• Celestial Machine Learning: Discovering the Planarity, Heliocentricity, and Orbital Equation of Mars with AI Feynman
• Finding Acceptable Parameter Regions of Stochastic Hill functions for Multisite Phosphorylation Mechanism
• Dimensionality Reduction and Dynamical Mode Recognition of Circular Arrays of Flame Oscillators Using Deep Neural Network
• Developing Parameter-Reduction Methods on a Biophysical Model of Auditory Hair Cells
• Learning effective good variables from physical data
• Deep Learning Alternative to Explicit Model Predictive Control for Unknown Nonlinear Systems
• KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework
• Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties
• Decoupling multivariate functions using a nonparametric filtered tensor decomposition
• Modeling compressed turbulent plasma with rapid viscosity variations
• Model discovery in the sparse sampling regime
• Universal set of Observables for Forecasting Physical Systems through Causal Embedding
• Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems
• OKRidge: Scalable Optimal k-Sparse Ridge Regression
• Autonomous Kinetic Modeling of Biomass Pyrolysis using Chemical Reaction Neural Networks
• Reversible and irreversible bracket-based dynamics for deep graph neural networks
• On the Predictive Capability of Dynamic Mode Decomposition for Nonlinear Periodic Systems with Focus on Orbital Mechanics
• Generalized Inverse Optimal Control and its Application in Biology
• Reconstruction of phase-amplitude dynamics from electrophysiological signals
• Data-driven input-to-state stabilization
• System stabilization with policy optimization on unstable latent manifolds
• Dimensional Reduction of Dynamical Systems by Machine Learning: Automatic Generation of the Optimum Extensive Variables and Their Time-Evolution Map
• Learning dynamical systems from data: Gradient-based dictionary optimization
• Remote Manipulation of Multiple Objects with Airflow Field Using Model-Based Learning Control
• Modeling Latent Non-Linear Dynamical System over Time Series
• Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics
• Variational inference formulation for a model-free simulation of a dynamical system with unknown parameters by a recurrent neural network
• Grammar-based Ordinary Differential Equation Discovery
• From Winter Storm Thermodynamics to Wind Gust Extremes: Discovering Interpretable Equations from Data
• Learning Chaotic Dynamics with Neuromorphic Network Dynamics
• Embedding physical symmetries into machine-learned reduced plasma physics models via data augmentation
• Symbolic identification of tensor equations in multidimensional physical fields
• Topological characterisation of a chaotic attractor with an additional branch generated from economic data
• Rodent: Relevance determination in differential equations
• Deriving thin-film averaged equations using computer algebra
• Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks
• Approximating the universal thermal climate index using sparse regression with orthogonal polynomials
• Hyperparameter Optimization in the Estimation of PDE and Delay-PDE models from data
• Data-driven nonlinear aerodynamics models with certifiably optimal boundedness properties
• Users' traffic on two-sided Internet platforms. Qualitative dynamics
• Sparse identification of effective microparticle interaction potential in dusty plasma from simulation data
• Forecasting Short-term Dynamics of Fair-Weather Cumuli using Dynamic Mode Decomposition
• FDR Control for Complex-Valued Data with Application in Single Snapshot Multi-Source Detection and DOA Estimation
• Improvement of system identification of stochastic systems via Koopman generator and locally weighted expectation
• Dynamical and statistical properties of estimated high-dimensional ODE models: The case of the Lorenz'05 type II model
• Physical Constraint Embedded Neural Networks for inference and noise regulation
• Sparsistent Model Discovery
• Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides
• Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
• Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing
• Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries
• Cluster-based network modeling -- automated robust modeling of complex dynamical systems
• Sparsity enabled cluster reduced-order models for control
• Identifying Physical Law of Hamiltonian Systems via Meta-Learning
• Disentangling Drift- and Control- Vector Fields for Interpretable Inference of Control-affine Systems
• Reconstruction of Delay Differential Equation via Learning Parameterized Dictionary
• Evolutionary-Based Sparse Regression for the Experimental Identification of Duffing Oscillator
• When Machine Learning Meets Multiscale Modeling in Chemical Reactions
• Discovering Phase Field Models from Image Data with the Pseudo-spectral Physics Informed Neural Networks
• Nonchaotic Models and Predictability of the Users' Volume Dynamics on Internet Platforms
• Revealing the intrinsic geometry of finite dimensional invariant sets of infinite dimensional dynamical systems
• Can Machine Learning Identify Governing Laws For Dynamics in Complex Engineered Systems ? : A Study in Chemical Engineering
• Deriving Compact Laws Based on Algebraic Formulation of a Data Set
• Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning
• Learning Gradient Flow: Using Equation Discovery to Accelerate Engineering Optimization
• Paradigm Shift Through the Integration of Physical Methodology and Data Science
• Dictionary-based model reduction for state estimation
• Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation
• Learning collision operators from plasma phase space data using differentiable simulators
• Information-based Variational Model Reduction of high-dimensional Reaction Networks
• A-priori sparsification of Galerkin-based reduced order models
• Physical reservoir computing using finitely-sampled quantum systems
• Comparing Dynamical Models Through Diffeomorphic Vector Field Alignment
• Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
• True Nonlinear Dynamics from Incomplete Networks
• Deep Koopman Economic Model Predictive Control of a Pasteurisation Unit
• The Machine Learning Approach to Moment Closure Relations for Plasma: A Review
• Online interpolation point refinement for reduced order models using a genetic algorithm
• Dynamics of reservoir computing for crises prediction
• Inference of Stochastic Dynamical Systems from Cross-Sectional Population Data
• Partial observations and conservation laws: Grey-box modeling in biotechnology and optogenetics
• Reduced Order Modeling using Shallow ReLU Networks with Grassmann Layers
• Reconstructing social sensitivity from evolution of content volume in Twitter
• A p-adaptive, implicit-explicit mixed finite element method for reaction-diffusion problems
• Dynamic mode decomposition for detecting oscillatory transient activity via sparsity and smoothness regularization
• Symbolic Learning of Interpretable Reduced-Order Models for Jumping Quadruped Robots
• Explainable Hierarchical Deep Learning Neural Networks (Ex-HiDeNN)
• Data-driven Discovery of Emergent Behaviors in Collective Dynamics
• Transforming physics-informed machine learning to convex optimization
• Koopman Eigenfunction-Based Identification and Optimal Nonlinear Control of Turbojet Engine
• Connecting implicit and explicit large eddy simulations of two-dimensional turbulence through machine learning
• An Approach to Sparse Continuous-time System Identification from Unevenly Sampled Data
• Data-Driven Contact-Aware Control Method for Real-Time Deformable Tool Manipulation: A Case Study in the Environmental Swabbing
• Coarse graining and reduced order models for plume ejection dynamics
• A Data-Driven Method for Microgrid System Identification: Physically Consistent Sparse Identification of Nonlinear Dynamics
• MagNet: Discovering Multi-agent Interaction Dynamics using Neural Network
• Characterizing nonlinear dynamics by contrastive cartography
• Sparse linear regression from perturbed data
• Physical discovery in representation learning via conditioning on prior knowledge: applications for ferroelectric domain dynamics
• MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS
• Forward Operator Estimation in Generative Models with Kernel Transfer Operators
• Relaxation dynamics of a quantum spin coupled to a topological edge state
• Estimation of spatial and time scales of collective behaviors of active matters through learning hydrodynamic equations from particle dynamics
• A Martingale-Free Introduction to Conditional Gaussian Nonlinear Systems
• Quantum Model-Discovery
• Projection-based model-order reduction via graph autoencoders suited for unstructured meshes
• Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering
• Object classification in analytical chemistry via data-driven discovery of partial differential equations
• Sparse Error Localization in Complex Dynamic Networks
• Discovering PDEs from Multiple Experiments
• $l_1$-based sparsification of energy interactions in two-dimensional turbulent flows
• Kernel Ordinary Differential Equations
• Towards Learning Stochastic Population Models by Gradient Descent
• Structured Online Learning-based Control of Continuous-time Nonlinear Systems
• A data-driven approach for modeling large-amplitude flow-induced oscillations of elastically mounted pitching wings
• Low-dimensional representation of intermittent geophysical turbulence with High-Order Statistics-informed Neural Networks (H-SiNN)
• Adaptive Latent Space Tuning for Non-Stationary Distributions
• Fully differentiable model discovery
• Compressed Compressor
• Learning Physical Concepts in Cyber-Physical Systems: A Case Study
• Phase space analysis of nonlinear wave propagation in a bistable mechanical metamaterial with a defect
• Learning stochastic filtering
• Stochastic Reaction-Diffusion Systems in Biophysics: Towards a Toolbox for Quantitative Model Evaluation
• Machine Learning Methods for Autonomous Ordinary Differential Equations
• Integrated utilization of equations and small dataset in the Koopman operator: applications to forward and inverse problems
• Interpretable neural network system identification method for two families of second-order systems based on characteristic curves
• Reaction-diffusion transport into core-shell geometry: Well-posedness and stability of stationary solutions
• Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach
• Electron correlation in semiconductors and insulators via symbolic regression
• Finite-time Lyaponov analysis of a trained reservoir computer
• Horizon-Constrained Rashomon Sets for Chaotic Forecasting
• Data-driven rational function neural networks: a new method for generating analytical models of rock physics
• Hyper-reduction-free reduced-order Newton solvers for projection-based model-order reduction of nonlinear dynamical systems