Related papers: Towards efficient quantum algorithms for diffusion…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
Diffusion models have achieved cutting-edge performance in image generation. However, their lengthy denoising process and computationally intensive score estimation network impede their scalability in low-latency and resource-constrained…
Many nonlinear PDEs have singular or oscillatory solutions or may exhibit physical instabilities or uncertainties. This requires a suitable concept of physically relevant generalized solutions. Dissipative measure-valued solutions have been…
We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.…
Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant…
The development of tailored materials for specific applications is an active field of research in chemistry, material science and drug discovery. The number of possible molecules that can be obtained from a set of atomic species grow…
Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into…
Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
The Carleman approach is well-known in the field of deterministic classical dynamics as a method to replace a finite number $d$ of non-linear differential equations by an infinite-dimensional linear system. Here this approach is applied to…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…