Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression

Abstract

Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws describing simple, low-dimensional systems with low levels of noise. Here we demonstrate that combining a data-driven methodology with some general physical principles enables discovery of a quantitatively accurate model of a non-equilibrium spatially-extended system from high-dimensional data that is both noisy and incomplete. We illustrate this using an experimental weakly turbulent fluid flow where only the velocity field is accessible. We also show that this hybrid approach allows reconstruction of the inaccessible variables -- the pressure and forcing field driving the flow.

Under review at Nature Communications

References in corpus (13)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data
• Discovering physical concepts with neural networks
• Model selection for dynamical systems via sparse regression and information criteria
• Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics
• Data-driven Discovery of Closure Models
• Forecasting Fluid Flows Using the Geometry of Turbulence
• Robust and optimal sparse regression for nonlinear PDE models
• Velocity Profile in a Two-Layer Kolmogorov-Like Flow
• Bifurcations in a Quasi-Two-Dimensional Kolmogorov-Like Flow
• Data-driven discovery of partial differential equation models with latent variables
• Unstable Equilibria and Invariant Manifolds in Quasi-Two-Dimensional Kolmogorov-like Flow
• Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow

Cited by in corpus (24)

• Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control
• PySINDy: A comprehensive Python package for robust sparse system identification
• A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge
• Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws
• Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)
• Learning hydrodynamic equations for active matter from particle simulations and experiments
• DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization
• Deep-learning assisted reduced order model for high-dimensional flow prediction from sparse data
• Data-driven discovery of active nematic hydrodynamics
• Data-driven discovery and extrapolation of parameterized pattern-forming dynamics
• Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case
• Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)
• Parsimony-Enhanced Sparse Bayesian Learning for Robust Discovery of Partial Differential Equations
• Machine learning of Kondo physics using variational autoencoders and symbolic regression
• Rheo-SINDy: Finding a Constitutive Model from Rheological Data for Complex Fluids Using Sparse Identification for Nonlinear Dynamics
• Text Entry for XR Trove (TEXT): Collecting and Analyzing Techniques for Text Input in XR
• Robust physics discovery via supervised and unsupervised pattern recognition using the Euler characteristic
• Discovering Nuclear Models from Symbolic Machine Learning
• Enhancing model identification with SINDy via nullcline reconstruction
• Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data
• Physics-informed AI and ML-based sparse system identification algorithm for discovery of PDE's representing nonlinear dynamic systems
• CTSR: Cartesian tensor-based sparse regression for data-driven discovery of high-dimensional invariant governing equations
• Sparse identification of effective microparticle interaction potential in dusty plasma from simulation data
• Symbolic identification of tensor equations in multidimensional physical fields