Related papers: On Fast Simulation of Dynamical System with Neural…

In this work, we present an early prototype of NeVer 2.0, a new system for automated synthesis and analysis of deep neural networks.NeVer 2.0borrows its design philosophy from NeVer, the first package that integrated learning, automated…

Concepts such as objects, patterns, and shapes are how humans understand the world. Building on this intuition, concept-based explainability methods aim to study representations learned by deep neural networks in relation to…

Model compression is essential in the deployment of large Computer Vision models on embedded devices. However, static optimization techniques (e.g. pruning, quantization, etc.) neglect the fact that different inputs have different…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

Deterministic approaches using iterative optimisation have been historically successful in diffeomorphic image registration (DiffIR). Although these approaches are highly accurate, they typically carry a significant computational burden.…

Using vanilla NeuralODEs to model large and/or complex systems often fails due two reasons: Stability and convergence. NeuralODEs are capable of describing stable as well as instable dynamic systems. Selecting an appropriate numerical…

Simulating physical systems using Partial Differential Equations (PDEs) has become an indispensible part of modern industrial process optimization. Traditionally, numerical solvers have been used to solve the associated PDEs, however…

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical…

High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Applications of reinforcement learning (RL) to stabilization problems of real systems are restricted since an agent needs many experiences to learn an optimal policy and may determine dangerous actions during its exploration. If we know a…

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…

We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…

Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust…

Turbulence simulation with classical numerical solvers requires high-resolution grids to accurately resolve dynamics. Here we train learned simulators at low spatial and temporal resolutions to capture turbulent dynamics generated at high…

While discrete-event simulators are essential tools for architecture research, design, and development, their practicality is limited by an extremely long time-to-solution for realistic applications under investigation. This work describes…

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to…