Related papers: DyMixOp: A Neural Operator Designed from a Complex…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…
A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims…
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Robust navigation in diverse environments and domains requires both accurate state estimation and transparent decision making. We present PhysNav-DG, a novel framework that integrates classical sensor fusion with the semantic power of…
Dynamic Data Driven Applications Systems (DDDAS) motivate the development of optimization approaches capable of adapting to streaming, heterogeneous, and asynchronous data from sensor networks. Many established optimization solvers, such as…
Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…
Deep neural networks (DNNs) have demonstrated promising results in various complex tasks. However, current DNNs encounter challenges with over-parameterization, especially when there is limited training data available. To enhance the…
Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…
Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
ADCME is a novel computational framework to solve inverse problems involving physical simulations and deep neural networks (DNNs). This paper benchmarks its capability to learn spatially-varying physical fields using DNNs. We demonstrate…