Exact terminal constraint for parabolic PDEs

Approximate solutions of parabolic terminal-value problems by neural networks in which the terminal condition holds exactly, and assess the effect of the extension of the terminal datum

Quick Facts

Type

Demonstrator

Status

Planned

Work Packages

WP2

Frameworks

PyTorch

1. Overview

Approximate solutions of parabolic terminal-value problems by neural networks in which the terminal condition holds exactly, and assess the effect of the extension of the terminal datum

1.1. Repository

access on request (remy.hosseinkhan@polytechnique.edu)

2. Technical Stack

2.1. Frameworks Used

  • PyTorch

2.2. Parallel Frameworks

  • GPU

3. Methods & Algorithms

3.1. WP2: Model Order Reduction & SciML

  • physics-informed NN with exact terminal constraint

4. Data Flow

4.1. Inputs

  • in-house

4.2. Outputs

  • JSON reports

  • PyTorch checkpoints

5. Benchmarking

5.1. Metrics

  • Analytical Solution Match

  • Time To Solution

5.2. Benchmark Scope

  • Single Node

6. Timeline

Milestone Date

Specification Due

N/A

Prototype Due

N/A

7. Team

Partners: IPP

Responsible: C.-A. Lehalle

8. Notes

Contributors: R. Hosseinkhan-Boucher, C.-A. Lehalle, N. Baradel. Validation: error against closed-form solutions for constant coefficients. Planned: wall-clock time per solve.