Ján Drgoňa

Junheng Li, Liang Wu, Sergio A. Esteban et al.

In humanoid motion control, model predictive control (MPC) offers physically grounded prediction and constraint handling, while reinforcement learning (RL) enables robust whole-body skills through large-scale simulation. However, using MPC inside RL often requires time-consuming problem construction or excessive training overhead, making such frameworks difficult to justify in practice. This work studies efficient training-time MPC guidance for humanoid locomotion and manipulation, termed MPC-RL. We introduce a centroidal-dynamics MPC reward formulation that leverages guidance from MPC trajectories in training time. To make this practical in massively parallel RL, we develop $π^n$MPC, a parallel-in-horizon and construction-free batched GPU MPC solver that operates directly on time-varying dynamics to avoid high memory usage and pre-compilation. Through a variety of comparative studies and hardware validations, we have found that MPC-RL achieves superior performance in locomotion and manipulation skills. The code base is available at https://github.com/junhengl/mpc-rl.

Truong X. Nghiem, Ján Drgoňa, Colin Jones et al.

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Sayak Mukherjee, Ján Drgoňa, Aaron Tuor et al.

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.

Liang Wu, Bo Yang, Junheng Li et al.

The alternating direction method of multipliers (ADMM) has gained increasing popularity in embedded model predictive control (MPC) due to its code simplicity and pain-free parameter selection. However, existing ADMM solvers either target general quadratic programming (QP) problems or exploit sparse MPC formulations via Riccati recursions, which are inherently sequential and therefore difficult to parallelize for long prediction horizons. This technical note proposes a novel \textit{parallel-in-horizon} and \textit{construction-free} nonlinear MPC algorithm, termed $π$MPC, which combines a new variable-splitting scheme with a velocity-based system representation in the ADMM framework, enabling horizon-wise parallel execution while operating directly on system matrices without explicit MPC-to-QP construction. Numerical experiments and accompanying code are provided to validate the effectiveness of the proposed method.

Ján Drgoňa, Sayak Mukherjee, Aaron Tuor et al.

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. Furthermore, we demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

Feras A. Batarseh, Priya L. Donti, Ján Drgoňa et al.

Climate change is one of the most pressing challenges of our time, requiring rapid action across society. As artificial intelligence tools (AI) are rapidly deployed, it is therefore crucial to understand how they will impact climate action. On the one hand, AI can support applications in climate change mitigation (reducing or preventing greenhouse gas emissions), adaptation (preparing for the effects of a changing climate), and climate science. These applications have implications in areas ranging as widely as energy, agriculture, and finance. At the same time, AI is used in many ways that hinder climate action (e.g., by accelerating the use of greenhouse gas-emitting fossil fuels). In addition, AI technologies have a carbon and energy footprint themselves. This symposium brought together participants from across academia, industry, government, and civil society to explore these intersections of AI with climate change, as well as how each of these sectors can contribute to solutions.

Hassan Iqbal, Xingjian Li, Tyler Ingebrand et al.

We introduce a differentiable framework for zero-shot adaptive control over parametric families of nonlinear dynamical systems. Our approach integrates a function encoder-based neural ODE (FE-NODE) for modeling system dynamics with a differentiable predictive control (DPC) for offline self-supervised learning of explicit control policies. The FE-NODE captures nonlinear behaviors in state transitions and enables zero-shot adaptation to new systems without retraining, while the DPC efficiently learns control policies across system parameterizations, thus eliminating costly online optimization common in classical model predictive control. We demonstrate the efficiency, accuracy, and online adaptability of the proposed method across a range of nonlinear systems with varying parametric scenarios, highlighting its potential as a general-purpose tool for fast zero-shot adaptive control.

Pietro Zanotta, Dibakar Roy Sarkar, Honghui Zheng et al.

Controlling partial differential equations (PDEs) with learning-based policies remains fundamentally limited by fixed-dimensional representations: policies trained for a specific sensor, actuator, or agent configuration typically fail when the configuration changes. This limitation is particularly severe in multi-agent PDE control, where policies do not scale across population sizes without retraining. We address this challenge by introducing Cardinality Invariant Neural Operator Control (CINOC), reformulating PDE control as an operator learning problem that maps state fields to continuous control functions and trains them end-to-end through differentiable PDE solvers, yielding policies that naturally adapt to varying sensor and actuator configurations. Remarkably, CINOC policies trained on small swarms exhibit cardinality invariance, allowing for zero-shot transfer to significantly larger populations as well as robustness to partial agent failure. This scalability arises from agents sharing a common policy and coordinating through their physical environment, which produces an emergent self-normalization effect. To explain this phenomenon, we provide a theorem grounded in mean-field theory demonstrating that policy gradients computed from finite-agent systems converge to those of a continuous control limit. Empirically, we validate CINOC on tracking, stabilization, and density transport across linear, nonlinear, chaotic, and turbulent PDEs.

Wenceslao Shaw Cortez, Soumya Vasisht, Aaron Tuor et al.

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, though convenient and quick to obtain, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their accuracy, generalization, and suitability for control.

Dibakar Roy Sarkar, Ján Drgoňa, Somdatta Goswami

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive Control (DPC)-a self-supervised learning framework for constrained neural control policies. The TI-DeepONet architecture learns temporal derivatives and couples them with numerical integrators, while the DPC algorithm uses automatic differentiation to compute policy gradients by backpropagating the expectations of the optimal control loss through the learned TI-DeepONet. This approach enables efficient offline optimization of neural policies without the need for online optimization or supervisory controllers. We empirically demonstrate the proposed method across diverse PDE systems, including the heat, the nonlinear Burgers', and the reaction-diffusion equations. The learned policies achieve target tracking, constraint satisfaction, and curvature minimization objectives, while generalizing across distributions of initial conditions and parameters. Moreover, we demonstrate four orders of magnitude acceleration at inference time compared to nonlinear model predictive control benchmarks. These results highlight the promise of operator learning for scalable model-based control of PDEs.

Weimin Huang, Natalie M. Isenberg, Ján Drgoňa et al.

Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly identify high-quality solutions within a short amount of time. Recently, a growing body of research has also used machine learning to accelerate solution methods for challenging combinatorial optimization problems. Despite the increasing popularity of these ML-guided methods, a large body of work has focused on Mixed-Integer Linear Programs (MILPs). MBQPs are challenging to solve due to the combinatorial complexity coupled with nonlinearities. This work proposes ML-guided primal heuristics for Mixed Binary Quadratic Programs (MBQPs) by adapting and extending existing work on ML-guided MILP solution prediction to MBQPs. We introduce a new neural network architecture for MBQP solution prediction and a new training data collection procedure. Moreover, we extend existing loss functions in solution prediction and propose to combine contrastive and weighted cross-entropy losses. We evaluate the methods on standard and real-world MBQP benchmarks and show that the developed ML-guided methods significantly outperform existing primal heuristics and state-of-the-art solvers. Furthermore, models trained with our proposed extension with combined losses outperform other ML-based methods adapted from MILPs and improve generalization in cross-regional inference on a real-world wind farm layout optimization problem.

Bo Tang, Elias B. Khalil, Ján Drgoňa

Mixed-integer nonlinear programs (MINLPs) arise in domains as diverse as energy systems and transportation, but are notoriously difficult to solve, particularly at scale. While learning-to-optimize (L2O) methods have been successful at continuous optimization, extending them to MINLPs is challenging due to integer constraints. To overcome this, we propose a novel L2O approach with two integer correction layers to ensure the integrality of the solution and a projection step to ensure the feasibility of the solution. We prove that the projection step converges, providing a theoretical guarantee for our method. Our experiments show that our methods efficiently solve MINLPs with up to tens of thousands of variables, providing high-quality solutions within milliseconds, even for problems where traditional solvers and heuristics fail. This is the first general L2O method for parametric MINLPs, finding solutions to some of the largest instances reported to date.

Xingjian Li, Kelvin Kan, Deepanshu Verma et al.

This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting in prohibitive computational costs for applications requiring frequent evaluation and adaptation. The proposed method learns a reusable set of neural basis functions that spans the control policy space, enabling efficient zero-shot adaptation to new tasks through either projection from data or direct mapping from problem specifications. The key idea is an offline-online decomposition: basis functions are learned once during offline imitation learning, while online adaptation requires only lightweight coefficient estimation. Numerical experiments across diverse dynamics, dimensions, and cost structures show our method delivers near-optimal performance with minimal overhead when generalizing across tasks, enabling semi-global feedback policies suitable for real-time deployment.

Renukanandan Tumu, Wenceslao Shaw Cortez, Ján Drgoňa et al.

Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive Control (DPC), a physics-informed machine learning methodology. We base our model on the Macroscopic Fundamental Diagram (MFD) and the Networked Macroscopic Fundamental Diagram (NMFD), offering a simplified representation of citywide traffic networks. Our approach ensures compliance with system constraints by construction. In empirical comparisons with existing state-of-the-art Model Predictive Control (MPC) methods, our approach demonstrates a 4 order of magnitude reduction in computation time and an up to 37% improvement in traffic performance. Furthermore, we assess the robustness of our controller to scenario shifts and find that it adapts well to changes in traffic patterns. This work proposes more efficient traffic control methods, particularly in large-scale urban networks, and aims to mitigate emissions and alleviate congestion in the future.

Aowabin Rahman, Ján Drgoňa, Aaron Tuor et al.

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods. We evaluate the inference speed and prediction performance of each method on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by an order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models. On the other hand, these performance gains come with a slight increase of computation at the inference time.

Ján Drgoňa, Sayak Mukherjee, Jiaxin Zhang et al.

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Christian Møldrup Legaard, Thomas Schranz, Gerald Schweiger et al.

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in data-driven modeling techniques, in particular neural networks have proven to provide an effective framework for solving a wide range of tasks. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.