Abstract: By leveraging neural networks, the emerging field of scientific machine learning (SciML) offers novel approaches to address complex problems governed by partial differential equations (PDEs) ...

Abstract: In this work, we propose a complex-valued neural operator (CV-NeuralOp) based on graph neural networks (GNN) to solve 2D wave equation. Inspired by the Green’s function method for solving ...

Have physics-informed neural networks been shown to solve partial differential equations whose solutions are non-separable functions? What suitable setups work?: deep/shallow NNs, what type of ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Math doesn’t have to be daunting, especially when your iPhone (or iPad) can do the heavy lifting. Tucked away inside iOS is a full-featured scientific calculator, ready to help you solve complex ...

Solving the 2-player Zero-Sum differential game using GARE (Kleinman) Solving the 2-player Zero-Sum differential game using Online Optimal Adaptive Control using Neural Network Solving the 2-player ...

Artificial intelligence-powered large language models (LLM) need to be trained on massive datasets to make accurate predictions—but what if researchers don't have enough of the right type of data? A ...