Project: Data-Efficient Machine Learning for Scientific Simulations

Edgar Torres, M.Sc. ~ PhD Researcher in Scientific Machine Learning             University of Stuttgart · IMPRS-IS · SimTech Cluster of Excellence                        Email | ResearchGate | ORCID |  Website
Project status: Ongoing

Overview

Numerical simulations are essential tools in science and engineering but are often computationally expensive, with complex simulations requiring days or weeks to complete. This becomes particularly challenging in applications involving repeated evaluations, such as design optimization, uncertainty quantification, or real-time decision-making.

This project develops data-efficient machine learning methods for scientific simulations, with a focus on surrogate modeling for partial differential equations (PDEs). Current research investigates adaptive Physics-Informed Neural Networks (PINNs), transfer learning, meta-learning, and few-shot learning strategies to efficiently adapt models across related simulation tasks while minimizing data requirements. The goal is to improve the efficiency, generalization, and adaptability of machine learning-based surrogate models for scientific computing applications.

Current Research

  • Amortized initialization methods for rapid adaptation of Physics-Informed Neural Networks
  • Hypernetwork-based low-rank representations for PDE surrogate models
  • Partition-of-unity adapters for local refinement of implicit PDE solutions
  • Data-efficient adaptation strategies for multi-query PDE applications

Publications & Preprints

Published Work

  • Torres, Edgar;  Schiefer, Jonathan; Niepert, Mathias: Adaptive Physics-informed Neural Networks: A Survey. In: Transactions on Machine Learning Research, 2025. [PDF][DOI]

Submitted Work

  • Torres, Edgar; Niepert, Mathias: Partition-of-Unity Adapters for Efficient Local Refinement of Implicit PDE Representations. Manuscript submitted for review, 2026.
  • Torres, Edgar; Niepert, Mathias: Amortized Physics-Informed Learning via Generative Initialization of Radial Basis Functions. Manuscript submitted for review, 2026.