arXiv subjects

Urban Fasel

Publications and source records attributed to Urban Fasel.

At least 19 recordsLinked to original sources

arXiv2026

HypEMBER: Hypernetwork-based Ensemble for Robust Policy Learning of Parametrized Dynamical Systems

In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties. High-dimensional state spaces, expensive numerical solvers, the partial knowledge of the governing equations, and the dependence on physical parameters that may be uncertain or difficult to estimate accurately, make the use of standard RL approaches computationally unfeasible. Indeed, lack of robustness and poor generalization across parameter variations are further amplified in presence of noisy or incomplete measurements, ultimately hampering control performance. To address these challenges, we introduce HypEMBER, a novel RL framework based on the combination of hypernetworks and ensemble learning. In the proposed approach, both the policy and value functions are represented through hypernetworks that generate the weights of the underlying models conditioned on the physical parameters of the system, thereby enabling parametric generalization across different dynamical regimes. In addition, an ensemble of policy and value approximators is employed to quantify epistemic uncertainty, leading to improved exploration strategies and enhanced robustness during and after training. The performance of the proposed framework is assessed on two representative parametrized control problems: (i) the one-dimensional Kuramoto-Sivashinsky equation and (ii) a particle-navigation task in a two-dimensional time-dependent gyre flow, focusing on robustness with respect to measurement noise and parameter misspecification. Numerical results demonstrate that HypEMBER consistently improves training stability and sample efficiency, while achieving superior robustness to uncertainties affecting both the system dynamics and the available observations, in comparison with state-of-the-art RL methods.

cs.LG↗

arXiv2026

An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications

Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known. Surrogate modeling techniques such as neural networks can capture the behavior of these systems, but they typically demand large training datasets that are difficult to obtain in engineering contexts and yield models with limited physical interpretability. The Sparse Identification of Nonlinear Dynamics (SINDy) method addresses both limitations by performing sparse regression over libraries of candidate nonlinear terms, recovering interpretable governing equations from comparatively small datasets. Although SINDy has been demonstrated extensively on canonical benchmark systems, its application to practical engineering problems is less widely documented. This tutorial introduces the SINDy method and progressively builds toward its main extensions, from noise-robust weak-form and ensembling-based variants to constrained and parametrizable formulations. The paper and the accompanying tutorial (available at https://github.com/paullililili/SINDy4Engineers) is organized in three parts: the first introduces the standard SINDy algorithm and progressively extends it, inviting readers without prior knowledge to follow each step and adapt the methods to their own problems; the remaining two parts present detailed case studies on (1) the system identification of an unmanned aerial vehicle and (2) a chaotic thermosyphon heat exchanger. Through these examples, we aim to demonstrate that SINDy is simple to implement yet flexible enough to serve as a valuable identification tool for advanced engineering applications.

cs.LG↗

arXiv2026

Co-Design of Aeroelastic Systems with Deep Reinforcement Learning

Control co-design considers the physical system and its controller together, enabling the strong coupling between system design and control to be uncovered and exploited. This is especially relevant in aeroelastic flight systems, where structural, aerodynamic, and control design choices jointly determine manoeuvrability and efficiency. This paper presents a model-free nested co-design framework for aeroelastic systems using deep reinforcement learning, in which a design-conditioned control policy is trained with proximal policy optimisation while an outer loop updates a distribution over candidate design parameters. The approach is evaluated on three case studies of increasing complexity: a spring-mass-damper system, a pitch-plunge-flap aerofoil, and a highly flexible high-aspect-ratio glider performing a thermal-soaring mission in a stochastic environment. Across these case studies, the framework is shown to progressively concentrate the design search towards high-performing regions and to outperform policies trained on randomly sampled designs. The results also show that reward shaping plays an important role in enabling stable learning in partially observed and stochastic environments. In the final glider case, the method jointly addresses wing design, flight control, and mission-level behaviour in the presence of aeroelastic coupling and atmospheric uncertainty. These results highlight the potential of model-free co-design for complex aeroelastic systems in which design, control, and mission objectives are tightly coupled.

eess.SY↗

arXiv2026

How Low Can You Go? Active Learning for Sparse Model Discovery in the Ultra-Low-Data Limit

Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions. However, data acquisition in real-world settings is often expensive. This work addresses this challenge by introducing an active learning strategy for dynamics discovery in the ultra-low data limit. Rather than sampling randomly, our method iteratively prioritizes regions that are most informative for model identification. This approach builds on Sparse Identification of Nonlinear Dynamics (SINDy), and utilizes an ensemble extension, E-SINDy, to estimate epistemic uncertainty and guide the sampling for both ordinary and partial differential equations (ODEs/PDEs). For ODEs, an exhaustive analysis is conducted on the Lorenz system across varying data budgets and noise levels. For PDEs, two systems with contrasting dynamical characteristics are examined: the Burgers' equation, where a sharp shock front creates a distinction between informative and uninformative regions, and the Kuramoto-Sivashinsky equation, which presents a more spatially complex sampling landscape. Across all scenarios, the proposed method accurately identifies the governing dynamics with significantly fewer data samples than random sampling.

cs.LG↗

arXiv2026

Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By using orthogonal sinusoidal test functions inspired by their prevalence in Modulating Function-based system identification, the weak-form sparse regression problem reduces to a regression over Fourier coefficients. Dominant frequencies are then selected via multitaper estimation of the frequency spectrum of the data. This formulation unifies weak-form learning and spectral estimation within a compact and flexible framework. We illustrate the effectiveness of this approach in numerical experiments across multiple chaotic and hyperchaotic ODE benchmarks.

cs.LG↗

arXiv2026

Robust Co-design Optimisation for Agile Fixed-Wing UAVs

Co-design optimisation of autonomous systems has emerged as a powerful alternative to sequential approaches by jointly optimising physical design and control strategies. However, existing frameworks often neglect the robustness required for autonomous systems navigating unstructured, real-world environments. For agile Unmanned Aerial Vehicles (UAVs) operating at the edge of the flight envelope, this lack of robustness yields designs that are sensitive to perturbations and model mismatch. To address this, we propose a robust co-design framework for agile fixed-wing UAVs that integrates parametric uncertainty and wind disturbances directly into the concurrent optimisation process. Our bi-level approach optimises physical design in a high-level loop while discovering nominal solutions via a constrained trajectory planner and evaluating performance across a stochastic Monte Carlo ensemble using feedback LQR control. Validated across three agile flight missions, our strategy consistently outperforms deterministic baselines. The results demonstrate that our robust co-design strategy inherently tailors aerodynamic features, such as wing placement and aspect ratio, to achieve an optimal trade-off between mission performance and disturbance rejection.

cs.RO↗

arXiv2025

Interconnection and Damping Assignment Passivity-Based Control using Sparse Neural ODEs

Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) is a nonlinear control technique that assigns a port-Hamiltonian (pH) structure to a controlled system using a state-feedback law. While IDA-PBC has been extensively studied and applied to many systems, its practical implementation often remains confined to academic examples and, almost exclusively, to stabilization tasks. The main limitation of IDA-PBC stems from the complexity of analytically solving a set of partial differential equations (PDEs), referred to as the matching conditions, which enforce the pH structure of the closed-loop system. However, this is extremely challenging, especially for complex physical systems and tasks. In this work, we propose a novel numerical approach for designing IDA-PBC controllers without solving the matching PDEs exactly. We cast the IDA-PBC problem as the learning of a neural ordinary differential equation. In particular, we rely on sparse dictionary learning to parametrize the desired closed-loop system as a sparse linear combination of nonlinear state-dependent functions. Optimization of the controller parameters is achieved by solving a multi-objective optimization problem whose cost function is composed of a generic task-dependent cost and a matching condition-dependent cost. Our numerical results show that the proposed method enables (i) IDA-PBC to be applicable to complex tasks beyond stabilization, such as the discovery of periodic oscillatory behaviors, (ii) the derivation of closed-form expressions of the controlled system, including residual terms in case of approximate matching, and (iii) stability analysis of the learned controller.

cs.RO↗

arXiv2025

HypeMARL: Multi-Agent Reinforcement Learning For High-Dimensional, Parametric, and Distributed Systems

Deep reinforcement learning has recently emerged as a promising feedback control strategy for complex dynamical systems governed by partial differential equations (PDEs). When dealing with distributed, high-dimensional problems in state and control variables, multi-agent reinforcement learning (MARL) has been proposed as a scalable approach for breaking the curse of dimensionality. In particular, through decentralized training and execution, multiple agents cooperate to steer the system towards a target configuration, relying solely on local state and reward information. However, the principle of locality may become a limiting factor whenever a collective, nonlocal behavior of the agents is crucial to maximize the reward function, as typically happens in PDE-constrained optimal control problems. In this work, we propose HypeMARL: a decentralized MARL algorithm tailored to the control of high-dimensional, parametric, and distributed systems. HypeMARL employs hypernetworks to effectively parametrize the agents' policies and value functions with respect to the system parameters and the agents' relative positions, encoded by sinusoidal positional encoding. Through the application on challenging control problems, such as density and flow control, we show that HypeMARL (i) can effectively control systems through a collective behavior of the agents, outperforming state-of-the-art decentralized MARL, (ii) can efficiently deal with parametric dependencies, (iii) requires minimal hyperparameter tuning and (iv) can reduce the amount of expensive environment interactions by a factor of ~10 thanks to its model-based extension, MB-HypeMARL, which relies on computationally efficient deep learning-based surrogate models approximating the dynamics locally, with minimal deterioration of the policy performance.

cs.LG↗

arXiv2025

Sparse Identification of Nonlinear Dynamics with Conformal Prediction

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in safety-critical applications. While various uncertainty quantification methods exist for SINDy, including Bayesian and ensemble approaches, this work explores the integration of Conformal Prediction, a framework that can provide valid prediction intervals with coverage guarantees based on minimal assumptions like data exchangeability. We introduce three applications of conformal prediction with Ensemble-SINDy (E-SINDy): (1) quantifying uncertainty in time series prediction, (2) model selection based on library feature importance, and (3) quantifying the uncertainty of identified model coefficients using feature conformal prediction. We demonstrate the three applications on stochastic predator-prey dynamics and several chaotic dynamical systems. We show that conformal prediction methods integrated with E-SINDy can reliably achieve desired target coverage for time series forecasting, effectively quantify feature importance, and produce more robust uncertainty intervals for model coefficients, even under non-Gaussian noise, compared to standard E-SINDy coefficient estimates.

cs.LG↗

arXiv2025

Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem

Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits (UPOs) have provided fundamental insight into chaotic dynamics as far back as the 19th century. The 3BP, a conservative system, is inherently challenging to sample due to its volume-preservation property. In this paper we present an interpretable data-driven approach for the state-dependent control of UPOs in the 3BP, through leveraging the inherent sensitivity of chaos and the local manifold structure. We overcome the sampling challenge by utilising prior knowledge of UPOs and a novel augmentation strategy. This enables sample-efficient discovery of a verifiable and accurate local Poincar\'{e} map in as few as 55 data points. We suggest that the Poincar\'{e} map is best discovered at a surface of section where the norm of the monodromy matrix, i.e. the local sensitivity to small perturbations, is the smallest. To stabilise the UPOs, we apply small velocity impulses once each period, determined by solving a convex system of linear matrix inequalities based on the linearised map. We constrain the norm of the decision variables used to solve this system, resulting in locally optimal velocity impulses directed along the local stable manifold. Critically, this behaviour is achieved in a computationally efficient manner. We demonstrate this sample-efficient and low-energy method across several orbit families in the 3BP, with potential applications ranging from robotics and spacecraft control to fluid dynamics.

math.DS↗

arXiv2025

SINDy on slow manifolds

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression problem becomes simultaneously computationally intractable and ill-conditioned. Although, in principle, modeling only the dynamics evolving on the underlying slow manifold addresses both of these challenges, the truncated fast variables have to be compensated by including higher-order nonlinearities as candidate terms for the model, leading to an explosive growth in the size of the SINDy library. In this work, we develop a SINDy variant that is able to robustly and efficiently identify slow-fast dynamics in two steps: (i) identify the slow manifold, that is, an algebraic equation for the fast variables as functions of the slow ones, and (ii) learn a model for the dynamics of the slow variables restricted to the manifold. Critically, the equation learned in (i) is leveraged to build a manifold-informed function library for (ii) that contains only essential higher-order nonlinearites as candidate terms. Rather than containing all monomials of up to a certain degree, the resulting custom library is a sparse subset of the latter that is tailored to the specific problem at hand. The approach is demonstrated on numerical examples of a snap-through buckling beam and the flow over a NACA 0012 airfoil. We find that our method significantly reduces both the condition number and the size of the SINDy library, thus enabling accurate identification of the dynamics on slow manifolds.

math.DS↗

arXiv2024

Future Pathways for eVTOLs: A Design Optimization Perspective

The rapid development of advanced urban air mobility, particularly electric vertical take-off and landing (eVTOL) aircraft, requires interdisciplinary approaches involving the future urban air mobility ecosystem. Operational cost efficiency, regulatory aspects, sustainability, and environmental compatibility should be incorporated directly into the conceptual design of aircraft and across operational and regulatory strategies. In this work, we apply a multidisciplinary design optimization framework for the conceptual design of eVTOL aircraft. The framework optimizes conventional design elements of eVTOL aircraft over a generic mission and integrates operational cost and an energy and battery-based emissions model to capture sustainability incentives of the designed system. We introduce a novel metric, the cross-transportation Figure of Merit (FoM), to compare the optimized eVTOL system with various competing road, rail, and air transportation modes in terms of sustainability, cost, and travel time. The framework incorporates regulatory, technical, and operational constraints to evaluate four distinct stakeholder-centric configurations: profit-maximizing, cost-minimizing, environmental impact-minimizing, and FoM-optimized designs. The results highlight the importance of integrating multiple operational disciplines into the design process, while underscoring the differing priorities of operators, regulators, and society.

eess.SY↗

arXiv2024

Interpretable low-order representation of eigenmode deformation in parameterized dynamical systems

Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics represent spatial patterns in vibration, temperature, or velocity fields associated with simple time dynamics. However, for systems that depend on one or more parameters, eigenmodes obtained for one set of parameter values are not necessarily dynamically relevant in other regions of parameter space. In this work, we formulate a method to obtain an optimal orthogonal basis of eigen-deformation modes (EDMs) that capture eigenmode variations across a range of parameter values. Through numerical examples of common parameterized dynamical systems in engineering, we show that EDMs are useful for parameterized model reduction and to provide physical insight into the effects of parameter changes on the underlying dynamics.

math.DS↗

arXiv2024

Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems

Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement Learning (RL), particularly Deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these issues, we propose a data-efficient, interpretable, and scalable Dyna-style Model-Based RL framework for PDE control, combining the Sparse Identification of Nonlinear Dynamics with Control (SINDy-C) algorithm and an autoencoder (AE) framework for the sake of dimensionality reduction of PDE states and actions. This novel approach enables fast rollouts, reducing the need for extensive environment interactions, and provides an interpretable latent space representation of the PDE forward dynamics. We validate our method on two PDE problems describing fluid flows - namely, the 1D Burgers equation and 2D Navier-Stokes equations - comparing it against a model-free baseline, and carrying out an extensive analysis of the learned dynamics.

cs.LG↗

arXiv2024

Sparsifying Parametric Models with L0 Regularization

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.

cs.LG↗

arXiv2024

Parametric PDE Control with Deep Reinforcement Learning and Differentiable L0-Sparse Polynomial Policies

Optimal control of parametric partial differential equations (PDEs) is crucial in many applications in engineering and science. In recent years, the progress in scientific machine learning has opened up new frontiers for the control of parametric PDEs. In particular, deep reinforcement learning (DRL) has the potential to solve high-dimensional and complex control problems in a large variety of applications. Most DRL methods rely on deep neural network (DNN) control policies. However, for many dynamical systems, DNN-based control policies tend to be over-parametrized, which means they need large amounts of training data, show limited robustness, and lack interpretability. In this work, we leverage dictionary learning and differentiable L$_0$ regularization to learn sparse, robust, and interpretable control policies for parametric PDEs. Our sparse policy architecture is agnostic to the DRL method and can be used in different policy-gradient and actor-critic DRL algorithms without changing their policy-optimization procedure. We test our approach on the challenging tasks of controlling parametric Kuramoto-Sivashinsky and convection-diffusion-reaction PDEs. We show that our method (1) outperforms baseline DNN-based DRL policies, (2) allows for the derivation of interpretable equations of the learned optimal control laws, and (3) generalizes to unseen parameters of the PDE without retraining the policies.

cs.LG↗

arXiv2024

SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in complex environments, such as stabilizing a tokamak fusion reactor or minimizing the drag force on an object in a fluid flow. However, DRL requires an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and flow control problems, including gust mitigation on a 3D NACA 0012 airfoil at $Re=1000$. SINDy-RL achieves comparable performance to modern DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a DRL policy.

cs.LG↗

arXiv2024

Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data

We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.

stat.ME↗