Related papers: A composable machine-learning approach for steady-…

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…

Seeing clearly with high resolution is a foundation of Large Multimodal Models (LMMs), which has been proven to be vital for visual perception and reasoning. Existing works usually employ a straightforward resolution upscaling method, where…

This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…

Differentiable programming allows for derivatives of functions implemented via computer code to be calculated automatically. These derivatives are calculated using automatic differentiation (AD). This thesis explores two applications of…

We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic…

This two-part work considers the minimum means square error (MMSE) estimation problem for a high dimensional multi-layer generalized linear model (ML-GLM), which resembles a feed-forward fully connected deep learning network in that each of…

We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…

Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…

Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is…

Gradient-domain machine learning (GDML) is an accurate and efficient approach to learn a molecular potential and associated force field based on the kernel ridge regression algorithm. Here, we demonstrate its application to learn an…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

Large-scale distributed computing infrastructures such as the Worldwide LHC Computing Grid (WLCG) require comprehensive simulation tools for evaluating performance, testing new algorithms, and optimizing resource allocation strategies.…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Machine learning (ML) applications become increasingly common in many domains. ML systems to execute these workloads include numerical computing frameworks and libraries, ML algorithm libraries, and specialized systems for deep neural…

Solving diverse partial differential equations (PDEs) is fundamental in science and engineering. Large language models (LLMs) have demonstrated strong capabilities in code generation, symbolic reasoning, and tool use, but reliably solving…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

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). In practical applications, challenges arise due…

Many emerging AI applications request distributed machine learning (ML) among edge systems (e.g., IoT devices and PCs at the edge of the Internet), where data cannot be uploaded to a central venue for model training, due to their large…