Related papers: PDE+: Enhancing Generalization via PDE with Adapti…
Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these…
We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Hypergraph neural networks (HGNNs) have shown remarkable potential in modeling high-order relationships that naturally arise in many real-world data domains. However, existing HGNNs often suffer from shallow propagation, oversmoothing, and…
This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…
Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs). However, their generalization capabilities across varying scenarios remain limited. To…
Single domain generalization is a challenging case of model generalization, where the models are trained on a single domain and tested on other unseen domains. A promising solution is to learn cross-domain invariant representations by…
Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under…
Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achieve this goal, we formulate DNN as an evolution operator from…
Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…
Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…
In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…
Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…
One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…
Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning…
Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…
Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling complex domains or incorporating empirical data. These…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…