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Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits…

We propose XPipe, an efficient asynchronous pipeline model parallelism approach for multi-GPU DNN training. XPipe is designed to use multiple GPUs to concurrently and continuously train different parts of a DNN model. To improve GPU…

We present DiffXPBD, a novel and efficient analytical formulation for the differentiable position-based simulation of compliant constrained dynamics (XPBD). Our proposed method allows computation of gradients of numerous parameters with…

Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many…

The Projection on Proper elements (PoPe) is a novel method of code control dedicated to 1) checking the correct implementation of models, 2) determining the convergence of numerical methods and 3) characterizing the residual errors of any…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

This work proposes a novel approach to transform any modern game engine pipeline, for optimized performance and enhanced user experiences in Extended Reality (XR) environments. Decoupling the physics engine from the game engine pipeline and…

Phase diagrams (PDs) illustrate the relative stability of competing phases under varying conditions, serving as critical tools for synthesizing complex materials. Reliable phase diagrams rely on precise free energy calculations, which are…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Neural networks offer powerful tools to solve partial differential equations (PDEs). We present a Variational Physics-Informed Neural Network (VPINN) designed for parabolic problems. Our approach combines a classical time discretization…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simulation. A difficulty with long-time simulations of traveling…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…

Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…