Related papers: FNODE: Flow-Matching for data-driven simulation of…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

Many engineered physical processes exhibit nonlinear but asymptotically stable dynamics that converge to a finite set of equilibria determined by control inputs. Identifying such systems from data is challenging: stable dynamics provide…

Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

The test-time optimization of scene flow - using a coordinate network as a neural prior - has gained popularity due to its simplicity, lack of dataset bias, and state-of-the-art performance. We observe, however, that although coordinate…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…

High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mapping between distributions across successive batches or time points form critical components of data analysis. The recent…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

Neural operators are becoming the default tools to learn solutions to governing partial differential equations (PDEs) in weather and ocean forecasting applications. Despite early promising achievements, significant challenges remain,…

Flow matching has emerged as a powerful generative framework, with recent few-step methods achieving remarkable inference acceleration. However, we identify a critical yet overlooked limitation: these models suffer from severe diversity…

Signed Distance Fields (SDFs) are a fundamental representation in robot motion planning. Their configuration-space counterpart, the Configuration Space Distance Field (CDF), directly encodes distances in joint space, offering a unified…

Key-point-based scene understanding is fundamental for autonomous driving applications. At the same time, optical flow plays an important role in many vision tasks. However, due to the implicit bias of equal attention on all points, classic…

Neural networks with physics based inductive biases such as Lagrangian neural networks (LNN), and Hamiltonian neural networks (HNN) learn the dynamics of physical systems by encoding strong inductive biases. Alternatively, Neural ODEs with…

Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…

Although GRPO substantially enhances flow matching models in human preference alignment of image generation, methods such as FlowGRPO and DanceGRPO still exhibit inefficiency due to the necessity of sampling and optimizing over all…

Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two…