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The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations on surfaces. The solvers are built on top of the well-known…
Computationally-intensive loops are the primary source of parallelism in scientific applications. Such loops are often irregular and a balanced execution of their loop iterations is critical for achieving high performance. However, several…
Neural Stochastic Differential Equations (Neural SDEs) have emerged as powerful mesh-free generative models for continuous stochastic processes, with critical applications in fields such as finance, physics, and biology. Previous…
Finite-difference methods are widely used in solving partial differential equations. In a large problem set, approximations can take days or weeks to evaluate, yet the bulk of computation may occur within a single loop nest. The modelling…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Domain-Specific Languages (DSLs) improve programmers productivity by decoupling problem descriptions from algorithmic implementations. However, DSLs for High-Performance Computing (HPC) have two additional critical requirements: performance…
This paper presents our work toward correct and efficient automatic differentiation of OpenMP parallel worksharing loops in forward and reverse mode. Automatic differentiation is a method to obtain gradients of numerical programs, which are…
This paper presents an overview of the functionalities and applications of Exasim, an open-source code for generating high-order discontinuous Galerkin codes to numerically solve parametrized partial differential equations (PDEs). The…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of…
We introduce Differential Performance Evaluation (DPE), a framework designed to reliably evaluate Large Language Models (LLMs) for efficient code generation. Traditional coding benchmarks often fail to provide reliable insights into code…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
Domain Specific Languages (DSLs) increase programmer productivity and provide high performance. Their targeted abstractions allow scientists to express problems at a high level, providing rich details that optimizing compilers can exploit…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…