Weak SINDy for partial differential equations
DA Messenger, DM Bortz - Journal of Computational Physics, 2021 - Elsevier
Abstract Sparse Identification of Nonlinear Dynamics (SINDy) is a method of system
discovery that has been shown to successfully recover governing dynamical systems from …
discovery that has been shown to successfully recover governing dynamical systems from …
Inference of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational …
We present a novel, fully three-dimensional approach to soft material characterization and
constitutive modeling with relevance to soft biological tissue. Our approach leverages recent …
constitutive modeling with relevance to soft biological tissue. Our approach leverages recent …
Data-driven discovery and extrapolation of parameterized pattern-forming dynamics
Pattern-forming systems can exhibit a diverse array of complex behaviors as external
parameters are varied, enabling a variety of useful functions in biological and engineered …
parameters are varied, enabling a variety of useful functions in biological and engineered …
The weak form is stronger than you think
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern
computational and applied mathematics. In this work we provide a survey of both the history …
computational and applied mathematics. In this work we provide a survey of both the history …
Label-free learning of elliptic partial differential equation solvers with generalizability across boundary value problems
X Zhang, K Garikipati - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
Traditional numerical discretization-based solvers of partial differential equations (PDEs) are
fundamentally agnostic to domains, boundary conditions and coefficients. In contrast …
fundamentally agnostic to domains, boundary conditions and coefficients. In contrast …
Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data
Pattern formation is a widely observed phenomenon in diverse fields including materials
physics, developmental biology and ecology, among many others. The physics underlying …
physics, developmental biology and ecology, among many others. The physics underlying …
Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations
Despite rapid progress in data acquisition techniques, many complex physical, chemical,
and biological systems remain only partially observable, thus posing the challenge to …
and biological systems remain only partially observable, thus posing the challenge to …
Scalable Bayesian optimization with randomized prior networks
Several fundamental problems in science and engineering consist of global optimization
tasks involving unknown high-dimensional (black-box) functions that map a set of …
tasks involving unknown high-dimensional (black-box) functions that map a set of …
[HTML][HTML] Machine learning of partial differential equations from noise data
Abstract Machine learning of partial differential equations from data is a potential
breakthrough to solve the lack of physical equations in complex dynamic systems, and …
breakthrough to solve the lack of physical equations in complex dynamic systems, and …
Investigating deep learning model calibration for classification problems in mechanics
Recently, there has been a growing interest in applying machine learning methods to
problems in engineering mechanics. In particular, there has been significant interest in …
problems in engineering mechanics. In particular, there has been significant interest in …