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We present a method for learning generalized Hamiltonian decompositions of ordinary differential equations given a set of noisy time series measurements. Our method simultaneously learns a continuous time model and a scalar energy function…
In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…
Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting…
Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
We introduce a self-consistent deep-learning framework which, for a noisy deterministic time series, provides unsupervised filtering, state-space reconstruction, identification of the underlying differential equations and forecasting.…
A longstanding goal in deep learning research has been to precisely characterize training and generalization. However, the often complex loss landscapes of neural networks have made a theory of learning dynamics elusive. In this work, we…
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…
Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…
Large neural networks trained on large datasets have become the dominant paradigm in machine learning. These systems rely on maximum likelihood point estimates of their parameters, precluding them from expressing model uncertainty. This may…
We propose a novel approach to model viscoelasticity materials using neural networks, which capture rate-dependent and nonlinear constitutive relations. However, inputs and outputs of the neural networks are not directly observable, and…
This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…
Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a…