arXiv subjects

Dion Häfner

Publications and source records attributed to Dion Häfner.

4 recordsLinked to original sources

arXiv2026

Mosaic: A Benchmark Suite for Differentiable Physics Solvers

Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented. Integration effort, computational cost, gradient accuracy, and numerical conditioning vary widely across solvers and are discoverable only by trial and error. We introduce Mosaic, an extensible benchmarking framework for differentiable PDE solvers that standardizes access to solver gradients. Each solver is packaged as a containerized component (Tesseract) exposing a uniform gradient API regardless of language or automatic differentiation (AD) strategy, enabling researchers to evaluate, compare, and build on non-trivial physical solvers. Our evaluation of 14 solvers across fluid dynamics, structural mechanics, and heat transfer demonstrates that the benchmark surfaces practically relevant differences: order-of-magnitude variation in computational cost and Jacobian conditioning, alongside structural incompatibilities that eliminate solvers from realistic tasks entirely. Despite this variation, all solvers that produce gradients converge to similar optima, indicating that the practical barriers are memory limits, numerical stability, and setup compatibility rather than gradient accuracy alone. Mosaic is open-source and available at https://github.com/pasteurlabs/mosaic.

physics.comp-ph↗

arXiv2025

Surrogate-Based Differentiable Pipeline for Shape Optimization

Gradient-based optimization of engineering designs is limited by non-differentiable components in the typical computer-aided engineering (CAE) workflow, which calculates performance metrics from design parameters. While gradient-based methods could provide noticeable speed-ups in high-dimensional design spaces, codes for meshing, physical simulations, and other common components are not differentiable even if the math or physics underneath them is. We propose replacing non-differentiable pipeline components with surrogate models which are inherently differentiable. Using a toy example of aerodynamic shape optimization, we demonstrate an end-to-end differentiable pipeline where a 3D U-Net full-field surrogate replaces both meshing and simulation steps by training it on the mapping between the signed distance field (SDF) of the shape and the fields of interest. This approach enables gradient-based shape optimization without the need for differentiable solvers, which can be useful in situations where adjoint methods are unavailable and/or hard to implement.

cs.CE↗

arXiv2023

Machine-Guided Discovery of a Real-World Rogue Wave Model

Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities of machine learning models for scientific discovery. This is because the goals of machine learning and science are generally not aligned. In addition to being accurate, scientific theories must also be causally consistent with the underlying physical process and allow for human analysis, reasoning, and manipulation to advance the field. In this paper, we present a case study on discovering a new symbolic model for oceanic rogue waves from data using causal analysis, deep learning, parsimony-guided model selection, and symbolic regression. We train an artificial neural network on causal features from an extensive dataset of observations from wave buoys, while selecting for predictive performance and causal invariance. We apply symbolic regression to distill this black-box model into a mathematical equation that retains the neural network's predictive capabilities, while allowing for interpretation in the context of existing wave theory. The resulting model reproduces known behavior, generates well-calibrated probabilities, and achieves better predictive scores on unseen data than current theory. This showcases how machine learning can facilitate inductive scientific discovery, and paves the way for more accurate rogue wave forecasting.

physics.geo-ph↗

arXiv2021

FOWD: A Free Ocean Wave Dataset for Data Mining and Machine Learning

The occurrence of extreme (rogue) waves in the ocean is for the most part still shrouded in mystery, as the rare nature of these events makes them difficult to analyze with traditional methods. Modern data mining and machine learning methods provide a promising way out, but they typically rely on the availability of massive amounts of well-cleaned data. To facilitate the application of such data-hungry methods to surface ocean waves, we developed FOWD, a freely available wave dataset and processing framework. FOWD describes the conversion of raw observations into a catalogue that maps characteristic sea state parameters to observed wave quantities. Specifically, we employ a running window approach that respects the non-stationary nature of the oceans, and extensive quality control to reduce bias in the resulting dataset. We also supply a reference Python implementation of the FOWD processing toolkit, which we use to process the entire CDIP buoy data catalogue containing over 4 billion waves. In a first experiment, we find that, when the full elevation time series is available, surface elevation kurtosis and maximum wave height are the strongest univariate predictors for rogue wave activity. When just a spectrum is given, crest-trough correlation, spectral bandwidth, and mean period fill this role.

physics.ao-ph↗