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

Accurate constitutive models of soft materials are crucial for understanding their mechanical behavior and ensuring reliable predictions in the design process. To this end, scientific machine learning research has produced flexible and…

Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is…

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…

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The network is used to simulate the…

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Since the seminal work of [9] and their Physics-Informed neural networks (PINNs), many efforts have been conducted towards solving partial differential equations (PDEs) with Deep Learning models. However, some challenges remain, for…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…

The article explains the convolutional LSTM (ConvLSTM) network in detail and introduces an improved auto-encoder version of the ConvLSTM network called AE-ConvLSTM. AE-ConvLSTM is also a sequence to sequence network that can predict long…

This paper proposes a physics-informed learning framework for a class of recurrent neural networks tailored to large-scale and networked systems. The approach aims to learn control-oriented models that preserve the structural and stability…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

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…

Accuracy in neural PDE solvers often breaks down not because of limited expressivity, but due to poor optimisation caused by ill-conditioning, especially in multi-fidelity and stiff problems. We study this issue in Physics-Informed Extreme…