Related papers: Neural Controlled Differential Equations with Quan…
Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
We present a hybrid transformer architecture that replaces discrete middle layers with a continuous-depth Neural Ordinary Differential Equation (ODE) block, enabling inference-time control over generation attributes via a learned steering…
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled…
Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning…
Simulating fluid dynamics on a quantum computer is intrinsically difficult due to the nonlinear and non-Hamiltonian nature of the Navier-Stokes equation (NSE). We propose a framework for quantum computing of fluid dynamics based on the…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
We prove controllability results for abstract systems of weakly coupled $N$ evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N-1$ controls. We give applications to…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic…
We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the…
Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…
It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum…
Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…
Simulating the dynamics of many-body quantum systems is a significant challenge, especially in higher dimensions where entanglement grows rapidly. Neural quantum states (NQS) offer a promising tool for representing quantum wavefunctions,…
Deep learning has proven to be a suitable alternative to least-squares (LSQ) fitting for parameter estimation in various quantitative MRI (QMRI) models. However, current deep learning implementations are not robust to changes in MR…
In this paper we apply quantum hydrodynamics (QHD) to study the quantum evolution of a system of spinning particles and particles that have the electric dipole moments EDM in the rotating reference frame. The method presented is based on…
We introduce a constructive method for mapping non-unitary dynamics to a weighted set of unitary operations. We utilize this construction to derive a new correspondence between real and imaginary time, which we term Imaginary Time Quantum…
We present a lightweighted neural PDE representation to discover the hidden structure and predict the solution of different nonlinear PDEs. Our key idea is to leverage the prior of ``translational similarity'' of numerical PDE differential…