control systems developers

Abstract: Physics-constrained machine learning (PCML) integrates domain knowledge, first-principles, and physical constraints into AI/ML models. In this work, we present a step-by-step tutorial of a modular PCML framework, KKT-HardNet, and illustrate how it could be used for hybrid modeling, process simulation, optimization and model predictive control in a single platform. KKT-HardNet combines fast inference capabilities of neural networks with guaranteed satisfaction of algebraic constraints through differential projection. It can handle heterogeneous data and enforce both linear and nonlinear equality and inequality constraints. The modular design supports custom neural-network backbones and user-defined projection mechanisms for PCML. To enable efficient end-to-end training, KKT-HardNet exploits implicit function theorem to backpropagate through the projection layer. This avoids computationally expensive automatic differentiation. This work also introduces an exact reduced-order Fischer-Burmeister reformulation and a primal-dual interior-point method as an alternative projection solve strategy. We also provide a diverse set of benchmarking problems for PCML in engineering applications. KKT-HardNet achieves orders of magnitude better performance in terms of both constraint satisfaction and inference time. The KKT-HardNet code and the benchmark datasets are available at https://github.com/souls-tamu/kkt-hardnet .

Abstract: Modern autonomous Cyber-Physical Systems (CPSs), such as self-driving cars, operate in increasingly complex environments while expected to maintain high reliability. The black-box nature of many of these systems makes it impossible to fully verify their behavior prior to deployment. When a failure occurs, it is important to analyze it to guide improvements to system robustness. A recent work introduced the novel concept of leveraging the framework of actual causality for CPS failure explanation. However, that work considered only a discrete, binary causal model that cannot capture continuous changes in system inputs. In this paper, we address these limitations by extending the actual causality framework with the notion of distance to account for the continuous characteristics of the system. Specifically, we introduce the novel concepts of distance-weighted actual cause and distance-weighted degree of responsibility, enabling causal influence to account for the magnitude of changes required to avoid a failure, rather than only its cardinality. While motivated by the continuous nature of CPSs, this constitutes a general extension of the theory of actual causality and enables more fine-grained analysis of continuous inputs in any causal model. Building on these notions, we present an efficient, practical, system-agnostic explanation-derivation algorithm that uses distance-weighted responsibility to guide the explanation search. We experimentally evaluate our approach across a number of environments from two autonomous-driving simulators with black-box neural controllers. The results show that the proposed extension provides more effective guidance than the current discrete approach.

Abstract: World action models (WAMs) predict actions and future observations, typically from a reconstruction-based representation that carries noisy, redundant information which can complicate downstream predictions. We introduce LeWAM, a bidirectional transformer for forward, backward, inverse dynamics and policy prediction, on a decoder-free JEPA latent trained end-to-end through all four modes. We see the following benefits: 1) Alignment: linear probes read robot and object state from LeWAM's latent better than from a regular Le World Model (a forward-only JEPA world model), while the latent ignores visual distractors as well as LeWM does and far better than a reconstruction-based WAM. 2) Acting: Closed-loop evaluations of LeWAM match a regular flow-matching policy trained on the same encoder at matched size, while also providing a world model. 3) Planning: Sampling raw actions when planning with WAMs lets MPC exploit dynamics-model inaccuracies; planning in the noise space of the policy head instead improves the closed-loop performance of these WAMs.

Abstract: As the input dimension $n$ grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck for function approximation: both rule count and parameter count grow exponentially with $n$. Traditional LCSs partition the $n$-dimensional input space directly, requiring $\mathcal{O}(m^n)$ rules for adequate coverage, where $m$ is the per-variable resolution. This article breaks from this paradigm by reorganizing rules dimension-wise, guided by the Kolmogorov-Arnold representation theorem: any continuous $n$-dimensional function can be expressed as a finite superposition of one-dimensional functions. The proposed Kolmogorov-Arnold Classifier System (KACS) decomposes the target function into one-dimensional subproblems and assigns a dedicated ruleset to each, reducing the worst-case rule count from $\mathcal{O}(m^n)$ to $\mathcal{O}(mn^2)$ and replacing $n$-dimensional local models with one-dimensional models requiring only two parameters per rule, independent of $n$. We also provide the first constructive proof that an LCS, namely KACS, is a universal approximator for continuous functions on compact domains. Evaluated against a direct $n$-dimensional input space partitioning approach under otherwise identical conditions, KACS achieves competitive accuracy in many settings while using only 2\% to 40\% of the parameters. Our implementation is available at https://github.com/YNU-NakataLab/KACS.

Abstract: High-fidelity simulations of time-dependent partial differential equations (PDEs) are computationally expensive, motivating data-driven reduced-order surrogates for many-query tasks such as uncertainty quantification, design optimization, data assimilation, and optimal control. However, existing surrogate models often exhibit poor temporal stability, which can lead to unstable rollouts and exploding gradients during backpropagation, especially in multistep long-horizon forecasting. To address this, we propose SMORE, a mesh-agnostic framework for model order reduction of time-dependent PDEs. Its latent dynamics are trained with Lyapunov-guided stability regularization, which promotes stable long-horizon rollouts. We provide theoretical guarantees under the stated structural assumptions. Beyond forecasting PDE evolution, the learned latent dynamics, which are interpretable and linear or linear-quadratic, could bring benefits for downstream tasks such as data assimilation and optimal control. Moreover, our framework is capable of predicting continuous PDE solution fields from sparse measurements of the initial condition. We evaluate SMORE on a range of problems, including wave propagation, the Navier-Stokes equations, and the shallow water equations. Our results show that it improves long-horizon rollout generalization and empirical robustness, and achieves competitive accuracy at comparable parameter budgets relative to competitive baselines including DINo, FNO, CNO, and Transolver.

Abstract: Lipschitz continuity is a fundamental principle in the design of certifiably robust deep neural networks (DNNs), wherein adjusting the Lipschitz constant, which quantifies network robustness, is of central theoretical importance. A standard approach to enforcing Lipschitz continuity requires each layer of a DNN to be Lipschitz continuous, thereby guaranteeing overall Lipschitz continuity. However, this layer-wise approach typically imposes overly conservative restrictions by producing a loose estimate of the overall Lipschitz constant, which limits the expressive capacity of the DNN and degrades empirical performance at a prescribed level of robustness. To overcome this loose estimation, the recently proposed LipKernel transfers information across layers to yield a much tighter overall Lipschitz bound than conventional layer-wise construction. In this paper, we extend this concept to cascaded state-space models (SSMs) to construct Lipschitz-continuous DNNs capable of modeling longer-term dependencies. The proposed architecture, named LipSSM, is theoretically justified and empirically evaluated.

Abstract: Dissipativity is a fundamental system-theoretic property closely related to stability, passivity, and input--output stability, and is particularly important in robotics, where learned dynamics models are often embedded within feedback control loops. However, most existing approaches for learning dissipative dynamics are based on continuous-time formulations, which require ODE solvers during training or inference and can therefore be computationally expensive. Moreover, because practical implementations are inherently discrete-time, direct discretization of a continuous-time passive system does not necessarily preserve passivity, motivating the need for explicit discrete-time guarantees. This study proposes a method for learning incrementally dissipative dynamics from input--output time-series data using a deep multilayer perceptron formulated directly in discrete time. Through a constrained parameterization and a dedicated training procedure, the proposed model guarantees incremental dissipativity by construction rather than through regularization. Lyapunov-based analysis establishes the corresponding dissipativity and stability guarantees, while simulations on robotic dynamical systems demonstrate competitive prediction accuracy, computational efficiency, and consistent preservation of incremental dissipativity compared with baseline methods.

Abstract: Learning in recurrent neural networks can fundamentally reshape their underlying dynamics, transforming initially chaotic activity into stable task-dependent behavior. We develop a non-equilibrium dynamical mean-field theory(DMFT) to describe this transition during learning. We show that a slow feedback-driven learning process generates an evolving effective feedback strength that drives the network through a transition from chaotic to stable dynamics defined by a bifurcation of the DMFT solution. By deriving the two-time correlation function throughout learning, we identify a critical feedback strength and a corresponding learning rate dependent critical time separating these regimes. The transition arises from the progressive deformation of an effective dynamical landscape by the growing learned feedback structure. Starting from the untrained state, the theory predicts the time evolution of the network output during training and shows quantitative agreement with numerical simulations.