相关论文: Flowers: A Warp Drive for Neural PDE Solvers

Plant classification is vital for ecological conservation and agricultural productivity, enhancing our understanding of plant growth dynamics and aiding species preservation. The advent of deep learning (DL) techniques has revolutionized…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections…

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as…

The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff…

The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a…

FPGAs have found their way into data centers as accelerator cards, making reconfigurable computing more accessible for high-performance applications. At the same time, new high-level synthesis compilers like Xilinx Vitis and runtime…

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…

Multi-step prediction is considered of major significance for time series analysis in many real life problems. Existing methods mainly focus on one-step-ahead forecasting, since multiple step forecasting generally fails due to accumulation…

We propose PROSE-FD, a zero-shot multimodal PDE foundational model for simultaneous prediction of heterogeneous two-dimensional physical systems related to distinct fluid dynamics settings. These systems include shallow water equations and…

Federated Learning (FL) is a decentralized machine learning paradigm where models are trained on distributed devices and are aggregated at a central server. Existing FL frameworks assume simple two-tier network topologies where end devices…

Transformers enable powerful content-based global routing via self-attention, but they lack an explicit local geometric prior along the sequence axis. As a result, the placement of locality-inducing modules in hybrid architectures has…

Vision Transformers (ViT) have recently demonstrated success across a myriad of computer vision tasks. However, their elevated computational demands pose significant challenges for real-world deployment. While low-rank approximation stands…

We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…

The performance of flow matching and diffusion models can be greatly improved at inference time using reward alignment algorithms, yet efficiency remains a major limitation. While several algorithms were proposed, we demonstrate that a…

Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…

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…