arXiv subjects

Hans Harder

Publications and source records attributed to Hans Harder.

9 recordsLinked to original sources

arXiv2026

Sparse Sensor Placement in Multi-Agent Reinforcement Learning Control of Rayleigh-B\'enard Convection

This paper studies sparse sensor placement for control of Rayleigh-B\'enard convection with multi-agent reinforcement learning. We train dense expert policies with windowed observations and distill sparse apprentice policies by supervised learning with grouped regularization on encoder input weights. The framework combines ordered non-convex grouped regularization and iterative reweighted grouped regularization, and uses a grouping construction that enforces consistent pruning across overlapping observation windows. Experiments with fixed and varying initial conditions show that Multi-Agent Transformer policies train more stably than proximal policy optimization baselines, while sparse apprentices retain control behavior comparable to dense experts. Sparsity results are strong for the proposed grouped methods across settings, including maximal sparsity in all fixed-initial-condition setting variants and maximal or near-maximal sparsity in varying-initial-condition setting variants. As an additional proof of concept, training from learned minimal sensor sets reduces per-agent observation size from 360 to 12 and preserves the overall training trend in simulation while reducing data throughput. The results provide both an interpretable basis for identifying control-relevant spatial regions and state components, and a practical pathway toward sensor-efficient control under realistic hardware constraints.

cs.MA↗

arXiv2025

Efficient probabilistic surrogate modeling techniques for partially-observed large-scale dynamical systems

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing various extensions to the flow matching paradigm that reduce the number of sampling steps. In this regard, it compares direct distillation, progressive distillation, adversarial diffusion distillation, Wasserstein GANs and rectified flows. Moreover, experiments are conducted on a set of challenging systems. In particular, we also address the challenge of directly predicting 2D slices of large-scale 3D simulations, paving the way for efficient inflow generation for solvers.

cs.LG↗

arXiv2025

Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders

The use of machine learning for modeling, understanding, and controlling large-scale physics systems is quickly gaining in popularity, with examples ranging from electromagnetism over nuclear fusion reactors and magneto-hydrodynamics to fluid mechanics and climate modeling. These systems - governed by partial differential equations - present unique challenges regarding the large number of degrees of freedom and the complex dynamics over many scales both in space and time, and additional measures to improve accuracy and sample efficiency are highly desirable. We present an end-to-end equivariant surrogate model consisting of an equivariant convolutional autoencoder and an equivariant convolutional LSTM using $G$-steerable kernels. As a case study, we consider the three-dimensional Rayleigh-B\'enard convection, which describes the buoyancy-driven fluid flow between a heated bottom and a cooled top plate. While the system is E(2)-equivariant in the horizontal plane, the boundary conditions break the translational equivariance in the vertical direction. Our architecture leverages vertically stacked layers of $D_4$-steerable kernels, with additional partial kernel sharing in the vertical direction for further efficiency improvement. We demonstrate significant gains in sample and parameter efficiency, as well as a better scaling to more complex dynamics. The accompanying code is available under https://github.com/FynnFromme/equivariant-rb-forecasting.

cs.LG↗

arXiv2024

Group-Convolutional Extended Dynamic Mode Decomposition

This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by finite-dimensional surrogates, e.g., via extended dynamic mode decomposition (EDMD), is challenging for high-dimensional systems due to computational constraints. To tackle this problem with a particular focus on EDMD, we demonstrate -- under suitable equivarance assumptions on the system and the observables -- that the optimal EDMD matrix is equivariant. That is, its action on states can be described by group convolutions and the generalized Fourier transform. We show that this structural property has many advantages for equivariant systems, in particular, that it allows for data-efficient learning, fast predictions and fast eigenfunction approximations. We conduct numerical experiments on the Kuramoto-Sivashinsky equation and a $\lambda$-$\omega$ spiraling wave system, both nonlinear partial differential equations, providing evidence of the effectiveness of this approach, and highlighting its potential for broader applications in dynamical systems analysis.

math.DS↗

arXiv2024

Solving Partial Differential Equations with Equivariant Extreme Learning Machines

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.

cs.LG↗

arXiv2024

On the continuity and smoothness of the value function in reinforcement learning and optimal control

The value function plays a crucial role as a measure for the cumulative future reward an agent receives in both reinforcement learning and optimal control. It is therefore of interest to study how similar the values of neighboring states are, i.e., to investigate the continuity of the value function. We do so by providing and verifying upper bounds on the value function's modulus of continuity. Additionally, we show that the value function is always H\"older continuous under relatively weak assumptions on the underlying system and that non-differentiable value functions can be made differentiable by slightly "disturbing" the system.

eess.SY↗

arXiv2023

Equivariance and partial observations in Koopman operator theory for partial differential equations

The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from measurements. This equally applies to ordinary, stochastic, and partial differential equations (PDEs). Until now, with a few exceptions only, the PDE case is mostly treated rather superficially, and the specific structure of the underlying dynamics is largely ignored. In this paper, we show that symmetries in the system dynamics can be carried over to the Koopman operator, which allows us to significantly increase the model efficacy. Moreover, the situation where we only have access to partial observations (i.e., measurements, as is very common for experimental data) has not been treated to its full extent, either. Moreover, we address the highly-relevant case where we cannot measure the full state, where alternative approaches (e.g., delay coordinates) have to be considered. We derive rigorous statements on the required number of observables in this situation, based on embedding theory. We present numerical evidence using various numerical examples including the wave equation and the Kuramoto-Sivashinsky equation.

math.DS↗

arXiv2023

A Unifying Formal Approach to Importance Values in Boolean Functions

Boolean functions and their representation through logics, circuits, machine learning classifiers, or binary decision diagrams (BDDs) play a central role in the design and analysis of computing systems. Quantifying the relative impact of variables on the truth value by means of importance values can provide useful insights to steer system design and debugging. In this paper, we introduce a uniform framework for reasoning about such values, relying on a generic notion of importance value functions (IVFs). The class of IVFs is defined by axioms motivated from several notions of importance values introduced in the literature, including Ben-Or and Linial's influence and Chockler, Halpern, and Kupferman's notion of responsibility and blame. We establish a connection between IVFs and game-theoretic concepts such as Shapley and Banzhaf values, both of which measure the impact of players on outcomes in cooperative games. Exploiting BDD-based symbolic methods and projected model counting, we devise and evaluate practical computation schemes for IVFs.

cs.GT↗

arXiv2020

SWITSS: Computing Small Witnessing Subsystems

Witnessing subsystems for probabilistic reachability thresholds in discrete Markovian models are an important concept both as diagnostic information on why a property holds, and as input to refinement algorithms. We present SWITSS, a tool for the computation of Small WITnessing SubSystems. SWITSS implements exact and heuristic approaches based on reducing the problem to (mixed integer) linear programming. Returned subsystems can automatically be rendered graphically and are accompanied with a certificate which proves that the subsystem is indeed a witness.

cs.LO↗