Related papers: Quantum framework for parameterizing partial diffe…

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…

In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…

In this paper, we investigate the fractional powers of block operator matrices, with a particular focus on their applications to partial differential equations (PDEs). We develop a comprehensive theoretical framework for defining and…

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…

The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Block encoding severs as an important data input model in quantum algorithms, enabling quantum computers to simulate non-unitary operators effectively. In this paper, we propose an efficient block-encoding protocol for sparse matrices based…

Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…

Variational Quantum Algorithms (VQAs) have emerged as a powerful class of algorithms that is highly suitable for noisy quantum devices. Therefore, investigating their design has become key in quantum computing research. Previous works have…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…

Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are…

The QED-C suite of Application-Oriented Benchmarks provides the ability to gauge performance characteristics of quantum computers as applied to real-world applications. Its benchmark programs sweep over a range of problem sizes and inputs,…

Achieving reliable performance on early fault-tolerant quantum hardware will depend on protocols that manage noise without incurring prohibitive overhead. We propose a novel framework that integrates quantum computation with the…

Quantum kernel methods are promising for near-term quantum ma- chine learning, yet their behavior under data corruption remains insuf- ficiently understood. We analyze how quantum feature constructions degrade under controlled additive…

We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the…

Quantum data encoding (QDE) enables faster com-putations than classical algorithms through superposition and en-tanglement. Circuit cutting and knitting are effective techniques for ameliorating current noisy quantum processing unit (QPUs)…

The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…