Related papers: Quantum-inspired space-time PDE solver and dynamic…
High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…
Quantum computing has demonstrated potential for solving complex optimization problems; however, its application to spatial regionalization remains underexplored. Spatial contiguity, a fundamental constraint requiring spatial entities to…
Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs)…
Recent advancements in deep learning have led to the development of various models for long-term multivariate time-series forecasting (LMTF), many of which have shown promising results. Generally, the focus has been on…
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated…
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with…
Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…
Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…
Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We…
Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…
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…
Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…
In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
We describe a method for simulating the real time evolution of extended quantum systems in two dimensions. The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder…
Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [Karimi and Tun\c{c}el, arXiv:1804.06925]. The current version of DDS accepts every combination of the following…
Engineering problems often involve solving partial differential equations (PDEs) over a range of similar problem setups with various state parameters. In traditional numerical methods, each problem is solved independently, resulting in many…