Related papers: Breaking the Discretization Barrier of Continuous …

In many scientific settings, acquiring complete observations of PDE coefficients and solutions can be expensive, hazardous, or impossible. Recent diffusion-based methods can reconstruct fields given partial observations, but require…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

This work introduces Physics-informed State-space neural network Models (PSMs), a novel solution to achieving real-time optimization, flexibility, and fault tolerance in autonomous systems, particularly in transport-dominated systems such…

This work presents novel discrete event-based simulation algorithms based on the Quantized State System (QSS) numerical methods. QSS provides attractive features for particle transportation processes, in particular a very efficient handling…

This work proposes a data-driven method for enabling the efficient, stable time-parallel numerical solution of systems of ordinary differential equations (ODEs). The method assumes that low-dimensional bases that accurately capture the time…

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…

Operating a robot in the open world requires a high level of robustness with respect to previously unseen environments. Optimally, the robot is able to adapt by itself to new conditions without human supervision, e.g., automatically…

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…

In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…

Aiming at improving performance of visual classification in a cost-effective manner, this paper proposes an incremental semi-supervised learning paradigm called Deep Co-Space (DCS). Unlike many conventional semi-supervised learning methods…

Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…

Recent deep network-based compressive sensing (CS) methods have achieved great success. However, most of them regard different sampling matrices as different independent tasks and need to train a specific model for each target sampling…

Extracting and predicting object structure and dynamics from videos without supervision is a major challenge in machine learning. To address this challenge, we adopt a keypoint-based image representation and learn a stochastic dynamics…

Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…

This study presents an innovative direct numerical simulation approach for complex particle systems with irregular shapes and large numbers. Using partially saturated methods, it accurately models arbitrary shapes, albeit at considerable…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2)…

Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…