Physics-informed fine-tuning of foundation models for partial differential equations

Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and distribution shifts. While fine-tuning has proven transformative in natural language processing, best practices for adapting PDE foundation models remain underexplored. Although physics-informed training has successfully trained accurate solvers across a wide range of PDE problems, its potential for fine-tuning data-based foundation models has not been systematically studied. In this work, we introduce a physics-informed fine-tuning framework that adapts pre-trained PDE foundation models by incorporating physical constraints (PDE residuals and boundary conditions) directly into the fine-tuning objective. This enables effective adaptation in data-scarce regimes while promoting physical consistency. We evaluate our method on a downstream task composed of an unseen PDE class and compare it with data-driven finetuning counterparts. Our results demonstrate that physics-informed fine-tuning achieves competitive accuracy without requiring PDE solutions for training. Furthermore, a hybrid fine-tuning strategy yields superior generalization to out-of-distribution scenarios when only minimal training data is available. These findings establish physics-informed fine-tuning as a scalable and data-efficient paradigm, providing a physically interpretable pathway for adapting foundation models in scientific machine learning.

Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings

We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various application, yet they are more challenging to hard-constrain in PINNs than Dirichlet conditions. Our method employs specific Fourier feature embeddings to directly incorporate Neumann boundary conditions into the neural network's architecture instead of learning them. The embedding can be naturally extended by high frequency modes to better capture high frequency phenomena. We demonstrate the efficacy of our approach through experiments on a diffusion problem, for which our method outperforms existing hard-constraining methods and classical PINNs, particularly in multiscale and high frequency scenarios.

Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimization

Advancements in Quantum Computing (QC) and Neural Combinatorial Optimization (NCO) represent promising steps in tackling complex computational challenges. On the one hand, Variational Quantum Algorithms such as QAOA can be used to solve a wide range of combinatorial optimization problems. On the other hand, the same class of problems can be solved by NCO, a method that has shown promising results, particularly since the introduction of Graph Neural Networks. Given recent advances in both research areas, we introduce Hamiltonian-based Quantum Reinforcement Learning (QRL), an approach at the intersection of QC and NCO. We model our ansatzes directly on the combinatorial optimization problem's Hamiltonian formulation, which allows us to apply our approach to a broad class of problems. Our ansatzes show favourable trainability properties when compared to the hardware efficient ansatzes, while also not being limited to graph-based problems, unlike previous works. In this work, we evaluate the performance of Hamiltonian-based QRL on a diverse set of combinatorial optimization problems to demonstrate the broad applicability of our approach and compare it to QAOA.

Continuously Adapting Random Sampling (CARS) for Power Electronics Parameter Design

To date, power electronics parameter design tasks are usually tackled using detailed optimization approaches with detailed simulations or using brute force grid search grid search with very fast simulations. A new method, named "Continuously Adapting Random Sampling" (CARS) is proposed, which provides a continuous method in between. This allows for very fast, and / or large amounts of simulations, but increasingly focuses on the most promising parameter ranges. Inspirations are drawn from multi-armed bandit research and lead to prioritized sampling of sub-domains in one high-dimensional parameter tensor. Performance has been evaluated on three exemplary power electronic use-cases, where resulting designs appear competitive to genetic algorithms, but additionally allow for highly parallelizable simulation, as well as continuous progression between explorative and exploitative settings.

Parameter Optimization of LLC-Converter with multiple operation points using Reinforcement Learning

The optimization of electrical circuits is a difficult and time-consuming process performed by experts, but also increasingly by sophisticated algorithms. In this paper, a reinforcement learning (RL) approach is adapted to optimize a LLC converter at multiple operation points corresponding to different output powers at high converter efficiency at different switching frequencies. During a training period, the RL agent learns a problem specific optimization policy enabling optimizations for any objective and boundary condition within a pre-defined range. The results show, that the trained RL agent is able to solve new optimization problems based on LLC converter simulations using Fundamental Harmonic Approximation (FHA) within 50 tuning steps for two operation points with power efficiencies greater than 90%. Therefore, this AI technique provides the potential to augment expert-driven design processes with data-driven strategy extraction in the field of power electronics and beyond.