Related papers: Neural SPDE solver for uncertainty quantification …

Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals…

Continuing advances in neural interfaces have enabled simultaneous monitoring of spiking activity from hundreds to thousands of neurons. To interpret these large-scale data, several methods have been proposed to infer latent dynamic…

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…

Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as…

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for…

Neural Bayes estimators are neural networks that approximate Bayes estimators in a fast and likelihood-free manner. Although they are appealing to use with spatial models, where estimation is often a computational bottleneck, neural Bayes…

We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth…

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context…

Backpropagation through (neural) SDE solvers is traditionally approached in two ways: discretise-then-optimise, which offers accurate gradients but incurs prohibitive memory costs; and optimise-then-discretise, which achieves constant…

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…

Efficiently solving Poisson equations on complex, irregular domains remains a fundamental challenge in scientific computing, as classical iterative solvers often suffer from prohibitive runtime due to ill-conditioned systems. While neural…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

By composing graphical models with deep learning architectures, we learn generative models with the strengths of both frameworks. The structured variational autoencoder (SVAE) inherits structure and interpretability from graphical models,…

Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…

Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…