WP2: Model Order Reduction, Surrogate, Scientific Machine Learning methods

WP2 develops non-intrusive approaches for ultra-fast surrogate models of complex physical problems, combining data-driven and model-driven techniques with a focus on physics-based neural network models.

Recent Highlights (2024-2025)

PINNs Innovation

Domain-decomposed PINNs with perfectly matched layers

Newton Solver Acceleration

Neural operators (FNO) accelerating Newton solvers: 80-200% CPU savings

Navier-Stokes ROMs

Reduced-order models for parametric Navier-Stokes

Exascale Optimization

Multi-fidelity surrogate-based optimization on 8000 GPUs (LUMI)

1. Objectives

WP2 uses non-intrusive approaches for designing ultra-fast surrogate models and strategies for leveraging these surrogates:

Data-Driven Techniques

  • Comparisons between reduced basis methods and neural network-based methods

  • Deep learning operators (FNO, DeepONet) for PDE solutions

  • Data-driven model order reduction without intrusive access to simulators

Model-Driven Techniques

  • Physics-informed neural networks (PINNs) respecting conservation laws

  • Neural operators learning PDE operators from data

  • Hybrid approaches combining physical constraints with data

2. Approach

Diagram

3. Key Tasks

T2.1: Physics-Driven Deep Learning

  • PINNs for PDEs with physical constraints

  • Domain decomposition strategies for large-scale problems

  • Perfectly matched layers for boundary conditions

T2.2: Neural Operators

  • Fourier Neural Operators (FNO) for parametric PDEs

  • DeepONet and operator learning frameworks

  • Accelerating Newton iterations with learned operators

T2.3: Data-Driven Model Order Reduction

  • Proper Orthogonal Decomposition (POD)

  • Dynamic Mode Decomposition (DMD)

  • Autoencoders for nonlinear dimensionality reduction

T2.4: Non-Intrusive Reduced Basis

  • Regression-based reduced basis methods

  • Greedy sampling for snapshot selection

  • A posteriori error estimation

T2.5: Multi-Fidelity Modeling

  • Coupling low-fidelity and high-fidelity models

  • Adaptive fidelity selection

  • Cost-accuracy trade-offs for large ensembles

T2.6: Super-Resolution Methods

  • Real-time models with spatial/temporal upsampling

  • Neural network-based mesh refinement

  • Generative models for fine-scale details

4. Leads & Partners

Lead Institution

Inria

Co-Leaders

UNISTRA, Sorbonne Université, CEA

Duration

Months 1-60

5. Deliverables

ID Title Due Dates

D2.1-S

Software packages for model reduction and scientific ML

M24, M36, M48, M60

D2.2-MR

Activity reports (included in annual report D0.2-TR)

M12, M24, M36, M48, M60

D2.3-B

Benchmarking analysis report

M12, M24, M36, M48, M60

6. Collaborations

  • WP1: Mesh adaptation guided by ML surrogates

  • WP3: Preconditioning with learned operators

  • WP4, WP5, WP6: Multi-fidelity models for inverse problems, optimization, and UQ

  • WP7: Showroom notebooks and benchmark integration