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This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…
We present a deep learning-based iterative approach to solve the discrete heterogeneous Helmholtz equation for high wavenumbers. Combining classical iterative multigrid solvers and convolutional neural networks (CNNs) via preconditioning,…
Identification of a groundwater contaminant source simultaneously with the hydraulic conductivity in highly-heterogeneous media often results in a high-dimensional inverse problem. In this study, a deep autoregressive neural network-based…
Deep models have recently emerged as promising tools to solve partial differential equations (PDEs), known as neural PDE solvers. While neural solvers trained from either simulation data or physics-informed loss can solve PDEs reasonably…
We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality.…
A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built…
Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour--whether electromagnetic, thermal, or mechanical--arises from modular substructure. Simulation and optimization of these materials…
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…
Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…