HiFiMagnet thermo-electric parameter inversion

Inverse application: estimate nonlinear electrical-conductivity, thermal-conductivity, contact and cooling parameters from voltage-drop, temperature and optional magnetic-field observations collected at several imposed-total-current operating points.

Quick Facts

Type

Extended Mini App

Status

Planned

Work Packages

WP1, WP2, WP3, WP4, WP6

Frameworks

Feel++, PETSc/TAO, HPDDM

1. Overview

Inverse application: estimate nonlinear electrical-conductivity, thermal-conductivity, contact and cooling parameters from voltage-drop, temperature and optional magnetic-field observations collected at several imposed-total-current operating points.

1.1. Repository

github.com/numpex/apps-feelpp

2. Technical Stack

2.1. Frameworks Used

  • Feel++

  • PETSc/TAO

  • HPDDM

2.2. Parallel Frameworks

  • MPI

  • Kokkos

  • GPU - HIP

3. Methods & Algorithms

3.1. WP1: Discretization

  • nonlinear thermo-electric finite elements

  • coupled PDE-scalar formulation

  • integral total-current boundary condition

3.2. WP2: Model Order Reduction & SciML

  • ROM

  • hyper-reduction

  • surrogate models

  • FOM/ROM switching for repeated forward and adjoint evaluations

3.3. WP3: Solvers

  • nonlinear block solvers

  • adjoint linear solves

  • PETSc/HPDDM preconditioning

3.4. WP4: Inverse Problems & Data Assimilation

  • PDE-constrained parameter inversion: weighted multi-experiment data misfit plus regularization; adjoint gradients; nonlinear least squares; parameter bounds; optional Gauss-Newton/Hessian actions and identifiability analysis

3.5. WP6: Uncertainty Quantification

  • measurement-noise modelling

  • uncertainty propagation

  • ensemble inversion

4. Data Flow

4.1. Inputs

  • Gmsh

  • JSON config

  • nonlinear material laws

  • imposed currents

  • voltage-drop and temperature observations

4.2. Outputs

  • Calibrated parameter vector or fields p*

  • forward and adjoint fields per experiment

  • predicted observables

  • residual decomposition

  • gradient/Hessian information

  • sensitivities

  • uncertainty estimates

  • objective histories

  • JSON/CSV reports

5. Benchmarking

5.1. Metrics

  • Taylor Gradient Test

  • Parameter Recovery Error

  • Observation Misfit By Observable

  • Regularization Contribution

  • Identifiability

  • Time To Inference

  • Pde Solves To Solution

  • Tao Iterations

  • Strong Scalability

  • Weak Scalability

  • Experiment Throughput

5.2. Benchmark Scope

  • Multi Node

  • Multi Gpu

  • Full System

  • Method Verification

  • Solver Scaling

  • Ensemble Mode

6. Timeline

Milestone Date

Specification Due

N/A

Prototype Due

N/A

7. Team

Partners: Unistra, LNCMI/CNRS

Responsible: C. Prud’homme; V. Chabannes

WP7 Engineer: Javier Cladellas (UNISTRA)

8. Notes

Mathematical specification. Unknown design p=(parameters or parameter fields for σ(T;p), k(T;p), electrical/thermal contacts and cooling). For experiments e=1,…,Ne with imposed total currents Ie, solve Fe(ye;p,Ie)=0 using the shared state y=(φ,T,ΔV). Minimize Jinv(p)=1/2 Σe [||WT(CT Te-dT,e)||² + wV|ΔVe-dV,e|² + wB||CB Be-dB,e||²] + αR(p), subject to pmin≤p≤pmax. Outputs are p*, reconstructed observables and state/adjoint fields—not operating controls. TAO provides the deterministic scalable baseline; experiments provide an outer level of parallelism.