131 citations · 339 across the 43 of their papers we have counts for
46 papers
An approach to encode divergence-free stress fields in neural approximations based on stress potentials
Mohammad S. Khorrami, Pawan Goyal, Soroush Motahari +5
The purpose of the current work is the development of an approach to account for quasi-static mechanical equilibrium in empirical (i.e., data-based) models for the stress field emp…
Reduced-Order Inference with Structure-Preserving Parametrization for Bending and Rotating Systems
Yevgeniya Filanova, Igor Pontes Duff, Pawan Goyal +1
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system…
On the representation of energy-preserving quadratic operators with application to Operator Inference
Leonidas Gkimisis, Igor Pontes Duff, Pawan Goyal +1
In this work, we investigate a skew-symmetric parameterization for energy-preserving quadratic operators. Earlier, [Goyal et al., 2023] proposed this parameterization to enforce en…
Structure-preserving learning for multi-symplectic PDEs
Süleyman Yıldız, Pawan Goyal, Peter Benner
This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations…
Active Sampling of Interpolation Points to Identify Dominant Subspaces for Model Reduction
Celine Reddig, Pawan Goyal, Igor Pontes Duff +1
Model reduction is an active research field to construct low-dimensional surrogate models of high fidelity to accelerate engineering design cycles. In this work, we investigate mod…
A physics-encoded Fourier neural operator approach for surrogate modeling of divergence-free stress fields in solids
Mohammad S. Khorrami, Pawan Goyal, Jaber R. Mianroodi +3
The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress fiel…
GS-PINN: Greedy Sampling for Parameter Estimation in Partial Differential Equations
Ali Forootani, Harshit Kapadia, Sridhar Chellappa +2
Partial differential equation parameter estimation is a mathematical and computational process used to estimate the unknown parameters in a partial differential equation model from…
GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations
Ali Forootani, Harshit Kapadia, Sridhar Chellappa +2
The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems b…
Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
Igor Pontes Duff, Pawan Goyal, Peter Benner
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often in…
Balanced Truncation of Descriptor Systems with a Quadratic Output
Jennifer Przybilla, Igor Pontes Duff, Pawan Goyal +1
This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstraß ca…
Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference
Ion Victor Gosea, Luisa Peterson, Pawan Goyal +3
In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This…
Roadmap on Data-Centric Materials Science
Stefan Bauer, Peter Benner, Tristan Bereau +58
Science is and always has been based on data, but the terms "data-centric" and the "4th paradigm of" materials research indicate a radical change in how information is retrieved, h…
A Robust SINDy Approach by Combining Neural Networks and an Integral Form
Ali Forootani, Pawan Goyal, Peter Benner
The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dyn…
Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics
Pawan Goyal, Süleyman Yıldız, Peter Benner
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex no…
Parameterized Interpolation of Passive Systems
Peter Benner, Pawan Goyal, Paul Van Dooren
We study the tangential interpolation problem for a passive transfer function in standard state-space form. We derive new interpolation conditions based on the computation of a def…
Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems
Süleyman Yildiz, Pawan Goyal, Peter Benner
This work discusses the model reduction problem for large-scale multi-symplectic PDEs with cubic invariants. For this, we present a linearly implicit global energy-preserving metho…
Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference
Pawan Goyal, Igor Pontes Duff, Peter Benner
Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineerin…
Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings
Süleyman Yildiz, Pawan Goyal, Thomas Bendokat +1
We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as no…
Rank-Minimizing and Structured Model Inference
Pawan Goyal, Benjamin Peherstorfer, Peter Benner
While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights ab…
Inference of Continuous Linear Systems from Data with Guaranteed Stability
Pawan Goyal, Igor Pontes Duff, Peter Benner
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from…
Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction
Pawan Goyal, Igor Pontes Duff, Peter Benner
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear…
An Operator Inference Oriented Approach for Mechanical Systems
Yevgeniya Filanova, Igor Pontes Duff, Pawan Goyal +1
Model-order reduction techniques allow the construction of low-dimensional surrogate models that can accelerate engineering design processes. Often, these techniques are intrusive,…
Generalized Quadratic Embeddings for Nonlinear Dynamics using Deep Learning
Pawan Goyal, Peter Benner
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for model…
A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems
Peter Benner, Pawan Goyal, Jan Heiland +1
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated…