Related papers: Training Deep Surrogate Models with Large Scale On…
Simulation-based plasma scenario development, optimization and control are crucial elements towards the successful deployment of next-generation experimental tokamaks and Fusion power plants. Current simulation codes require extremely…
Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE)…
Scientific machine learning is increasingly being spoken of as universal emulators for classical numerical solvers for multi-scale partial differential equations, but most apparent successes can be explained by facts that also define their…
In this paper, we investigate the applications of operator learning, specifically DeepONet, for solving nonlinear partial differential equations (PDEs). Unlike conventional function learning methods that require training separate neural…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…
Partial differential equations (PDEs) are a central tool for modeling the dynamics of physical, engineering, and materials systems, but high-fidelity simulations are often computationally expensive. At the same time, many scientific…
Calibration of neural networks is a topical problem that is becoming more and more important as neural networks increasingly underpin real-world applications. The problem is especially noticeable when using modern neural networks, for which…
The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…
This paper presents a methodological framework for training, self-optimising, and self-organising surrogate models to approximate and speed up multiobjective optimisation of technical systems based on multiphysics simulations. At the hand…
In this paper, we present a deep surrogate model for learning the Green's function associated with the reaction-diffusion operator in rectangular domain. The U-Net architecture is utilized to effectively capture the mapping from source to…
Neural operators have recently grown in popularity as Partial Differential Equation (PDE) surrogate models. Learning solution functionals, rather than functions, has proven to be a powerful approach to calculate fast, accurate solutions to…
Solving complex problems requires continuous effort in developing theory and practice to cope with larger, more difficult scenarios. Working with surrogates is normal for creating a proxy that realistically models the problem into the…
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…
Deep learning approaches are increasingly used to tackle forecasting tasks involving datasets with multiple univariate time series. A key factor in the successful application of these methods is a large enough training sample size, which is…
In this work, we describe a novel approach to building a neural PDE solver leveraging recent advances in transformer based neural network architectures. Our model can provide solutions for different values of PDE parameters without any need…
We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensional parameter spaces. The contributions of this paper are…
This work presents a physics-informed deep learning-based super-resolution framework to enhance the spatio-temporal resolution of the solution of time-dependent partial differential equations (PDE). Prior works on deep learning-based…
Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…