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

Physics-aware deep learning (PADL) has gained popularity for use in complex spatiotemporal dynamics (field evolution) simulations, such as those that arise frequently in computational modeling of energetic materials (EM). Here, we show that…

We present MRPARCv2, Multi-resolution Physics-Aware Recurrent Convolutional Neural Network, designed to model complex flows by embedding the structure of advection-diffusion-reaction equations and leveraging a multi-resolution architecture.…

Physics-aware deep learning (PADL) enables rapid prediction of complex physical systems, yet current convolutional neural network (CNN) architectures struggle with highly nonlinear flows. While scaling model size addresses complexity in…

Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

Recurrent neural networks (RNNs) have recently been extensively applied to model the time-evolution in fluid dynamics, weather predictions, and even chaotic systems thanks to their ability to capture temporal dependencies and sequential…

The thermo-mechanical response of shock-initiated energetic materials (EM) is highly influenced by their microstructures, presenting an opportunity to engineer EM microstructure in a "materials-by-design" framework. However, the current…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

Spatio-temporal dynamics of physical processes are generally modeled using partial differential equations (PDEs). Though the core dynamics follows some principles of physics, real-world physical processes are often driven by unknown…

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…

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network.…

Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…

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 second…

In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

Predictive Physics has been historically based upon the development of mathematical models that describe the evolution of a system under certain external stimuli and constraints. The structure of such mathematical models relies on a set of…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

We propose a physics-constrained convolutional neural network (PC-CNN) to solve two types of inverse problems in partial differential equations (PDEs), which are nonlinear and vary both in space and time. In the first inverse problem, we…