Workpackage

WP0 - Project Management

Objective

Oversee overall project coordination, scientific and technical management, and administrative tasks.

Key Topics

• —Communication and coordination
• —Risk and conflict management
• —Financial and administrative monitoring
• —Governance and compliance

Description

WP0 establishes the project's governance structure and ensures smooth operation by integrating contributions from all other work packages. It is responsible for maintaining communication within the consortium, handling administrative duties, and ensuring compliance with funding agreements.

Workpackage

WP1 - Discretization

Objective

Develop robust techniques for mesh generation, adaptive refinement, high-order discretization, and efficient time integration for multiphysics simulations.

Key Topics

• —Mesh generation (including nonconforming methods)
• —Adaptive mesh refinement strategies
• —High-order and spectral discretization
• —Parallel-in-time and asynchronous time-integration methods

Description

WP1 focuses on the creation and adaptation of mesh representations and discretization techniques that reduce communication overhead and increase computational intensity—crucial features for exascale applications.

Workpackage

WP2 - Model Order Reduction, Surrogates & Scientific Machine Learning

Objective

Develop fast surrogate models and reduced-order methods by integrating data-driven and physics-based machine learning techniques.

Key Topics

• —Neural Galerkin methods
• —Physics-Informed Neural Networks (PINNs)
• —Non-intrusive reduced basis approaches
• —Multi-fidelity modeling

Description

WP2 aims to accelerate simulations by reducing computational complexity while preserving essential features of the physical models. Advanced machine learning tools are leveraged to develop effective surrogate models and reduction techniques.

Workpackage

WP3 - Solvers for Linear Algebra & Multiphysics

Objective

Design scalable solvers for large sparse linear systems and coupled multiphysics problems on exascale architectures.

Key Topics

• —Domain decomposition methods
• —Mixed precision arithmetic and error control
• —Adaptive solver strategies
• —Robust multiphysics coupling techniques

Description

WP3 focuses on developing robust and efficient solver technologies. The goal is to handle the computational challenges of both mono-physics and coupled multiphysics simulations on modern exascale hardware.

Workpackage

WP4 - Inverse Problems & Data Assimilation

Objective

Integrate observational data with physical models to solve inverse problems through deterministic and stochastic methods.

Key Topics

• —Variational and ensemble-based data assimilation
• —Stochastic differential equations (SDEs/SPDEs)
• —Multi-fidelity strategies for inverse problems
• —Optimized observation error models

Description

WP4 addresses the challenge of blending simulation data with real-world observations. Its goal is to improve model predictions and enable enhanced decision-making through advanced data assimilation and inverse problem methodologies.

Workpackage

WP5 - Optimization

Objective

Develop exascale optimization algorithms for tackling combinatorial, continuous, and mixed optimization challenges, including shape optimization and AutoML.

Key Topics

• —Decomposition-based optimization strategies
• —Surrogate-based and multi-fidelity optimization
• —Shape optimization techniques
• —Optimization for AI (AutoML)

Description

WP5 is dedicated to designing innovative optimization methods that leverage exascale computational capabilities. These methods will facilitate faster and more accurate solutions for complex design, control, and decision-making problems.

Workpackage

WP6 - Uncertainty Quantification

Objective

Quantify uncertainties in complex multiscale simulations and understand their impact on predictive modeling.

Key Topics

• —Kernel-based sensitivity analysis
• —Surrogate modeling for uncertainty quantification
• —High-dimensional integration and uncertainty propagation
• —Multi-arithmetic and multi-fidelity approaches

Description

WP6 develops techniques to assess and manage uncertainties within simulation models. This work is essential for ensuring that predictions are reliable and for guiding improvements in model fidelity.

Workpackage

WP7 - Showroom, Benchmarking & Co-Design Coordination

Objective

Coordinate the integration, testing, and benchmarking of methods and software developed across the Exa-MA project, ensuring interoperability and high performance.

Key Topics

• —Development of benchmarking frameworks and non-regression tests
• —Creation of demonstrators, mini-apps, and proxy-apps
• —Training and dissemination activities
• —Agile co-design and continuous integration

Description

WP7 acts as the central hub for evaluating and validating the project's outputs. It provides a structured environment for testing, benchmarking, and training, ensuring that all developed components work cohesively on exascale architectures.

Software

Arcane

Arcane is a development environment for parallel numerical calculation codes. It supports the architectural aspects of a calculation code, such as data structures for meshing and parallelism, as well as more environment-related aspects such as dataset configuration.

NumPEx software criteria

Software

CGAL

CGAL is a software project that provides easy access to efficient and reliable geometric algorithms in the form of a C++ library.

NumPEx software criteria

Software

Composyx

Composyx is a linear algebra C++ library focused on composability. Its purpose is to allow the user to express a large pannel of algorithms using a high-level interface to range from laptop prototypes to many node supercomputer parallel computations.

NumPEx software criteria

Software

Fabulous

Versatile and flexible numerical library that implements Block Krylov iterative schemes for the solution of linear systems of equations with multiple right-hand sides. This Library currently implements various variants of Block Krylov iterative solvers: BCG (Block Conjugate Gradient), BF-BCG (Breadown Free BCG), BGCR (Block Generalized Conjugate Residual), BGMRES (Block General Minimum Residual), IB-BGMRES (BGMRES with inexact breakdown), BGMRES-DR (BGMRES with deflated restarting), IB-BGMRES-DR (BGMRES with inexact breakdown and deflated restarting), IB-BGCRO-DR (Block Generalized Conjugate Residual Method with Inner Orthogonalization with inexact breakdown and deflated restarting). A particular attention is paid to internal numerical kernels such as those associated with the least-square solution where block Incremental QR factorization variants are implemented.

NumPEx software criteria

Software

Feel++

Feel is an open-source, high-performance C framework for solving complex PDE and ODE-based mathematical models using advanced Galerkin methods (finite element, discontinuous Galerkin, and spectral methods) and efficient reduced-order modeling (ROM) techniques, including Reduced Basis (RB), Proper Orthogonal Decomposition (POD), and Empirical Interpolation Methods (EIM). It features specialized application toolboxes (CFD, CSM, FSI, thermoelectric, Maxwell), modern parallel computing with seamless Python integration (Pybind11), and extensive DevOps support (CI/CD, benchmarking, and containers). Feel++ is used in academia and industry for multiphysics simulations, inverse problems, uncertainty quantification, data assimilation, and machine learning applications.

NumPEx software criteria

Software

FreeFEM

FreeFEM is a partial differential equation solver for non-linear multi-physics systems in 2D and 3D using the finite element method. Problems involving partial differential equations from several branches of physics such as fluid-structure interactions require interpolations of data on several meshes and their manipulation within one program. FreeFEM includes a fast interpolation algorithm and a language for the manipulation of data on multiple meshes. It is written in C++ and the FreeFEM language is a C++ idiom.

NumPEx software criteria

Software

Hawen

Hawen solves time-harmonic wave problems for acoustic and elastic media using the Hybridizable Discontinuous Galerkin (HDG) method for discretization. It combines mpi and OpenMP parallelism to solve large-scale applications such as Earth's imaging and helioseismology. It can handle the forward problem (propagation of waves) as well as the inverse problem (parameter identification).

NumPEx software criteria

Software

HPDDM

HPDDM is an efficient implementation of various domain decomposition methods (DDM) such as one- and two-level Restricted Additive Schwarz (RAS) methods, the Finite Element Tearing and Interconnecting (FETI) method, and the Balancing Domain Decomposition (BDD) method.

NumPEx software criteria

Software

MaHyCo

MaHyCo is a inite volume code for solving hydrodynamic equations: Lagrangian or Eulerian simulations.

NumPEx software criteria

Software

MUMPS

MUMPS is a high-performance software package for solving large sparse linear systems, supporting a wide range of matrix types and arithmetic precisions, with advanced features like parallel processing, iterative refinement, out-of-core computation, and interfaces for Fortran, C, Matlab, and Scilab.

NumPEx software criteria

Software

PaStiX

PaStiX (Parallel Sparse matriX package) is a scientific library that provides a high performance parallel solver for very large sparse linear systems based on direct methods. Numerical algorithms are implemented in single or double precision (real or complex) using LLt, LDLt and LU with static pivoting (for non symmetric matrices having a symmetric pattern). This solver also provides some low-rank compression methods to reduce the memory footprint and/or the time-to-solution.

NumPEx software criteria

Software

PETSc

PETSc, the Portable, Extensible Toolkit for Scientific Computation, pronounced PET-see, is for the scalable (parallel) solution of scientific applications modeled by partial differential equations (PDEs).

NumPEx software criteria

Software

Qr_mumps

Qr_mumps is a software package for the solution of sparse, linear systems on multicore computers. It implements a direct solution method based on the QR factorization of the input matrix. Therefore, it is suited to solving sparse least-squares problems and to computing the minimum-norm solution of sparse, underdetermined problems. It can obviously be used for solving square problems in which case the stability provided by the use of orthogonal transformations comes at the cost of a higher operation count with respect to solvers based on, e.g., the LU factorization. Qr_mumps supports real and complex, single or double precision arithmetic.

NumPEx software criteria

Software

Samurai

The use of mesh adaptation methods in numerical simulation allows to drastically reduce the memory footprint and the computational costs. There are different kinds of methods: AMR patch-based, AMR cell-based, multiresolution cell-based or point-based, …

Different open source software is available to the community to manage mesh adaptation: AMReX for patch-based AMR, p4est and pablo for cell-based adaptation.

The strength of samurai is that it allows to implement all the above mentioned mesh adaptation methods from the same data structure. The mesh is represented as intervals and a set algebra allows to efficiently search for subsets among these intervals. Samurai also offers a flexible and pleasant interface to easily implement numerical methods.

NumPEx software criteria

Software

TRUST Platform

TRUST is a thermalhydraulic software package for CFD simulations. This software was originally designed for conduction, incompressible single-phase, and Low Mach Number (LMN) flows with a robust Weakly-Compressible (WC) multi-species solver. However, a huge effort has been conducted recently, and now TRUST is able to simulate real compressible multi-phase flows.

NumPEx software criteria

Software

Uranie

The Uranie platform is an open-source framework developed at the Alternative Energies and Atomic Energy Commission (CEA), in the nuclear energy division, in order to deal with uncertainty propagation, surrogate models, optimisation issues, code calibration, etc. This platform benefits from both its dependencies and from personal developments, to offer an efficient data handling model, a C++ and Python interface, advanced graphi graphical tools, several parallelisation solutions, etc. These methods can then be applied to many kinds of code (considered as black boxes by Uranie) so to many fields of physics as well.

NumPEx software criteria