Related papers: Flowers: A Warp Drive for Neural PDE Solvers

Diffusion models deliver state-of-the-art generative performance across diverse modalities but remain computationally expensive due to their inherently iterative sampling process. Existing training-free acceleration methods typically…

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other…

Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…

Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…

In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engineering tasks suffers from significant computational…

Attention mechanisms have emerged as transformative tools in core AI domains such as natural language processing and computer vision. Yet, their largely untapped potential for modeling intricate physical systems presents a compelling…

Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under…

We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Scene flow represents the 3D motion of every point in the dynamic environments. Like the optical flow that represents the motion of pixels in 2D images, 3D motion representation of scene flow benefits many applications, such as autonomous…

A novel toolbox named FLOreS is presented for intuitive design of fractional order controllers (FOC) using industry standard loop shaping technique. This will allow control engineers to use frequency response data (FRD) of the plant to…

We propose a novel type of nonlinear solver acceleration for systems of nonlinear partial differential equations (PDEs) that is based on online/adaptive learning. It is applied in the context of multiphase flow in porous media. The proposed…

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g.,…

Neural networks are known to give better performance with increased depth due to their ability to learn more abstract features. Although the deepening of networks has been well established, there is still room for efficient feature…

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We…

The combination of spiking neural networks and event-based vision sensors holds the potential of highly efficient and high-bandwidth optical flow estimation. This paper presents the first hierarchical spiking architecture in which motion…

Computational Fluid Dynamics (CFD) is used in the design and optimization of gas turbines and many other industrial/ scientific applications. However, the practical use is often limited by the high computational cost, and the accurate…

Deep learning paradigms, such as PINNs and neural operators, have significantly advanced the solving of PDEs. However, they often struggle to capture the continuous integral nature of physical systems, relying either on pointwise residuals…