Related papers: Autoregressive Renaissance in Neural PDE Solvers
Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…
The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved…
Optimization-based PDE solvers that minimize scalar loss functions have gained increasing attention in recent years. These methods either define the loss directly over discrete variables, as in Optimizing a Discrete Loss (ODIL), or…
Graph Neural Networks have achieved impressive results across diverse network modeling tasks, but accurately estimating uncertainty on graphs remains difficult, especially under distributional shifts. Unlike traditional uncertainty…
In recent years, new methods for solving partial differential equations (PDEs) such as Monte Carlo random walk methods have gained considerable attention. However, due to the lack of hardware-intrinsic randomness in the conventional von…
In this paper, we propose a domain-decomposition-based deep learning (DL) framework, named transient-CoMLSim, for accurately modeling unsteady and nonlinear partial differential equations (PDEs). The framework consists of two key…
The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
Data over non-Euclidean manifolds, often discretized as surface meshes, naturally arise in computer graphics and biological and physical systems. In particular, solutions to partial differential equations (PDEs) over manifolds depend…
We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
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…
In recent years, there has been a notable surge in research on machine learning techniques for combinatorial optimization. It has been shown that learning-based methods outperform traditional heuristics and mathematical solvers on the…
Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…
The concept of the path-dependent partial differential equation (PPDE) was first introduced in the context of path-dependent derivatives in financial markets. Its semilinear form was later identified as a non-Markovian backward stochastic…
Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as…
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…
In recent years, machine learning and deep learning approaches such as artificial neural networks have gained in popularity for the resolution of automatic puzzle resolution problems. Indeed, these methods are able to extract high-level…
Deep neural networks have become invaluable tools for supervised machine learning, e.g., classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in…