Related papers: Learning on the Temporal Tangent Bundle for Physic…

Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to…

The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

We develop a numerical framework, the Deep Tangent Bundle (DTB) method, that is suitable for computing solutions of evolutionary partial differential equations (PDEs) in high dimensions. The main idea is to use the tangent bundle of an…

In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bundle filters and tangent bundle neural networks (TNNs) based…

Time-fractional differential equations offer a robust framework for capturing intricate phenomena characterized by memory effects, particularly in fields like biotransport and rheology. However, solving inverse problems involving fractional…

Recent theoretical works based on the neural tangent kernel (NTK) have shed light on the optimization and generalization of over-parameterized networks, and partially bridge the gap between their practical success and classical 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…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Value approximation using deep neural networks is at the heart of off-policy deep reinforcement learning, and is often the primary module that provides learning signals to the rest of the algorithm. While multi-layer perceptron networks are…

Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

This paper presents a constrained policy gradient algorithm. We introduce constraints for safe learning with the following steps. First, learning is slowed down (lazy learning) so that the episodic policy change can be computed with the…

Turbulence is notoriously difficult to model due to its multi-scale nature and sensitivity to small perturbations. Classical solvers of turbulence simulation generally operate on finer grids and are computationally inefficient. In this…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy…

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…

Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency…

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…