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Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be…

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…

Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations,…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

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 convergence of statistical learning and molecular physics is transforming our approach to modeling biomolecular systems. Physics-informed machine learning (PIML) offers a systematic framework that integrates data-driven inference with…

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…

Physics-informed neural networks (PINNs) constitute a flexible approach to both finding solutions and identifying parameters of partial differential equations. Most works on the topic assume noiseless data, or data contaminated with weak…

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

Physics-informed neural networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding governing physical laws directly into the training objective. Recent advances in quantum machine…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…

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…

The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be generally improved either by increasing the number of training points or by improving the…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…