Related papers: Refining Fast Calorimeter Simulations with a Schr\…
For a fixed flow-based generative model under a small inference budget, sample quality can depend strongly on where the sampler spends its few function evaluations. Flow matching and Schr\"odinger bridges define probability paths, yet their…
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
This paper introduces scour physics-inspired neural networks (SPINNs), a hybrid physics-data-driven framework for bridge scour prediction using deep learning. SPINNs integrate physics-based, empirical equations into deep neural networks and…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Despite the continuous advancements in size and robustness of real quantum devices, reliable large-scale quantum computers are not yet available. Hence, classical simulation of quantum algorithms remains crucial for testing new methods and…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
Chemical modelling serves two purposes in dynamical models: accounting for the effect of microphysics on the dynamics and providing observable signatures. Ideally, the former must be done as part of the hydrodynamic simulation but this…
This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…
Accurate simulation of atomic systems has the potential to revolutionize the design of molecules and materials. Unfortunately, exact solutions of the Schr\"odinger equation scale as O(N!) and remain inaccessible for systems with more than a…
The accurate and precise extraction of information from a modern particle physics detector, such as an electromagnetic calorimeter, may be complicated and challenging. In order to overcome the difficulties we propose processing the detector…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
Incompressible fluid flow around a cylinder is one of the classical problems in fluid-dynamics with strong relevance with many real-world engineering problems, for example, design of offshore structures or design of a pin-fin heat…
Fluid simulation is an important research topic in computer graphics (CG) and animation in video games. Traditional methods based on Navier-Stokes equations are computationally expensive. In this paper, we treat fluid motion as point cloud…
Spiking neural networks (SNNs), central to computational neuroscience and neuromorphic machine learning (ML), require efficient simulation and gradient-based training. While AI accelerators offer promising speedups, gradient-based SNNs…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…