Related papers: Physics-Informed Geometric Operators to Support Su…

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…

Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated that incorporating Lie point symmetry information can…

Generative adversarial networks (GAN) have recently been used for a design synthesis of mechanical shapes. A GAN sometimes outputs physically unreasonable shapes. For example, when a GAN model is trained to output airfoil shapes that…

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical…

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…

We introduce CODES, a benchmark for comprehensive evaluation of surrogate architectures for coupled ODE systems. Besides standard metrics like mean squared error (MSE) and inference time, CODES provides insights into surrogate behaviour…

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…

In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction…

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote…

This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to…

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical…

Mesh-based numerical solvers are an important part in many design tool chains. However, accurate simulations like computational fluid dynamics are time and resource consuming which is why surrogate models are employed to speed-up the…

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based…

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…

Bayesian optimization (BO) methods often rely on the assumption that the objective function is well-behaved, but in practice, this is seldom true for real-world objectives even if noise-free observations can be collected. Common approaches,…

Traditional deep learning compilers rely on heuristics for subgraph generation, which impose extra constraints on graph optimization, e.g., each subgraph can only contain at most one complex operator. In this paper, we propose AGO, a…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Many learning-based approaches have difficulty scaling to unseen data, as the generality of its learned prior is limited to the scale and variations of the training samples. This holds particularly true with 3D learning tasks, given the…