Related papers: PARCv2: Physics-aware Recurrent Convolutional Neur…

Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…

Model-based Reinforcement Learning and Control have demonstrated great potential in various sequential decision making problem domains, including in robotics settings. However, real-world robotics systems often present challenges that limit…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…

Generalizing across disparate physical laws remains a fundamental challenge for artificial intelligence in science. Existing deep-learning solvers are largely confined to single-equation settings, limiting transfer across physical regimes…

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the \textbf{physics} of the underlying weather evolution or the \textbf{topology} of the Earth's surface. In light of…

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

To comprehend complex systems with multiple states, it is imperative to reveal the identity of these states by system outputs. Nevertheless, the mathematical models describing these systems often exhibit nonlinearity so that render the…

Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

Climate models are essential to understand and project climate change, yet long-standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid-scale processes, particularly…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…