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Andrea Manzoni

Publications and source records attributed to Andrea Manzoni.

At least 19 recordsLinked to original sources
arXiv2026

Real-time optimal control with shallow recurrent decoder networks

Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require several system simulations, which are often computationally demanding due to the high-dimensionality of the underlying spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time closed-loop controller for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on a few optimal examples given by an expert demonstrator, SHRED-ROM mimics the expert behavior with effective distributed control actions in new scenarios, alleviating the curse of dimensionality. Moreover, a sensor forecaster is synthesized and used to close the loop at the latent level, thus efficiently mitigating possible sensor failures or delays. The performance of the proposed optimal control strategy is finally assessed on three challenging high-dimensional cases dealing with either parametric density control or fluid flow control.

cs.LG↗
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

Physics-enhanced reinforcement learning for real-time optimal control of dynamical systems

Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems. However, RL algorithms are sample inefficient and require a large number of interaction with the environment to synthesize optimal control strategies. Consequently, applications of RL are typically limited to sparse sensors and actuators due to the curse of dimensionality entailed by the exploration-exploitation dilemma in high-dimensional spaces. In this work, we bridge RL and traditional optimal control for dynamical system with a novel Physics-EnhAnced Reinforcement Learning (PEARL) paradigm tailored to the control of high-dimensional and parametric dynamical systems, exploiting the differentibility of their dynamics. Specifically, PEARL employs an actor-adjoint algorithm that leverages automatic differentiation to compute policy gradients over short horizons and adjoint-based sensitivities of future returns approximated via neural networks, significantly reducing the number of environment interactions, while mitigating long-term gradient instabilities. Through two challenging parametric navigation problems in unsteady flows, we show that PEARL (i) effectively exploits differentiable environments to outperform state-of-the-art RL algorithms, (ii) is sample efficient, thanks to the physics-guided policy learning, (iii) generalizes across multiple scenarios, which is crucial when dealing with parametric systems, and (iv) enables scaling RL to high-dimensional state and action spaces, without requiring low-dimensional state representations or multi-agent strategies.

cs.LG↗
arXiv2026

Flow-aware Optimal Navigation in Unsteady Flows through Reinforcement Learning

Autonomous robotic navigation in nonstationary time-varying fluid flows remains a fundamental challenge due to partial observability and the unpredictability of realistic environments. While classical optimal control frameworks employed in robotics require unrealistic a-priori global flow knowledge, biological systems are able to navigate successfully by exploiting localized sensory cues. In this work we present a reinforcement learning approach using the TD3 algorithm to train autonomous agents to reach arbitrary targets within a parametric, chaotic double-gyre flow. To investigate optimal sensory mechanisms, we evaluate five bio-inspired observation strategies based on relative position, local velocity or local vorticity measures, and short-term memory variants. Additionally, we analyze the impact of providing agents with explicit global flow parameters. Numerical results demonstrate that an agent that is able to sense and remember a set number of flow velocity measures achieves the highest performance. The experiments reveal a trade-off in sensor utility: velocity-aware agents optimize energy efficiency, whereas vorticity sensors provide superior structural mapping and achieve better target proximity. Incorporating explicit global flow parameters is shown to decrease navigation performance. This behavior suggests that reinforcement learning-based autonomous systems develop more robust and general policies when restricted to implicit flow representations. The presented results offer insights for improving the transition of bio-inspired robotic navigation from simulation to real-world environments.

cs.RO↗
arXiv2026

Multi-Fidelity SINDy: Sparse Discovery of Nonlinear Dynamical Systems with Fidelity-Weighted Measurements

Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity. Measurement uncertainty may vary across repeated observations, sensing devices, or even within a single experiment. This work addresses the problem of discovering nonlinear dynamical systems from such inhomogeneous data. We extend the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework to account for variable noise levels by combining Ensemble SINDy and Weak SINDy within a weighted regression formulation derived from generalized least squares. A statistical justification for the weighting strategy is also provided. The methodology is validated on several benchmark systems, including ordinary and partial differential equations. In addition, we show the benefit of multi-fidelity integration for forecasting the dynamics of a double pendulum system. The results confirm that the proposed approach mitigates the adverse effects of heteroscedastic noise and that repeated, low-cost, low-quality measurements can improve model recovery, in some cases matching or outperforming reconstructions obtained using only high-fidelity data.

cs.LG↗
arXiv2026

Multi-Agent Digital Twins for Strategic Decision-Making using Active Inference

Active Inference is an emerging framework providing a quantitative account of behavioral processes in neuroscience and a principled approach to decision-making under uncertainty. Its application to agency problems is natural, offering an autopoietic interpretation of action while addressing classical challenges such as the exploration-exploitation trade-off. Recently, Active Inference has been applied to digital twin scenarios for adaptive and predictive modeling of complex systems. In this work, we extend Active Inference to multi-agent digital twins in which agents interact within a shared environment while maintaining decentralized generative models. Our multi-agent framework features two innovations: (i) contextual inference to improve adaptability in dynamic environments, and (ii) the integration of streaming machine learning within agents' generative structures, enabling tunable goal-oriented behavior while preserving efficiency and scalability. The framework is illustrated through a Cournot competition example, providing a digital twin representation of a socio-economic system and highlighting its potential for coordinated decision-making in multi-agent contexts.

cs.CE↗
arXiv2026

MoE-Sieve: Routing-Guided LoRA for Efficient MoE Fine-Tuning

Standard LoRA fine-tuning of Mixture-of-Experts (MoE) models applies adapters to every expert, yet our profiling shows that per-layer expert routing is highly skewed: a small subset of experts handles most tokens in each layer, while many others are rarely activated ("cold"). We propose MoE-Sieve, a simple routing-guided framework for LoRA fine-tuning, and pair it with a systematic profiling study of expert routing across architectures and tasks. The method is simple: profile routing counts on a small calibration set, select the top-k most-routed experts per layer, and apply LoRA only to those experts. Across two architecturally distinct MoE models and three diverse tasks, tuning only the top 25% routed experts per layer remains competitive with full LoRA, with mean differences within +/-1 percentage point across all conditions. This reduces LoRA trainable parameters by 70-73%, adapter checkpoint size by 71-73%, and wall-clock training time by up to 50%. We also observe a non-monotonic relationship between expert count and seed-to-seed variance, consistent with the hypothesis that adapting cold experts can introduce gradient noise without improving accuracy. Further ablations show that random expert selection at matched budget is about 2.5 percentage points worse, indicating that the routing signal matters, while greedy per-layer budget optimization does not improve over uniform top-k.

cs.LG↗
arXiv2026

Active Digital Twins via Active Inference

Digital twins are transforming engineering and applied sciences by enabling real-time monitoring, simulation, and predictive analysis of physical systems and processes. However, conventional digital twins rely primarily on passive data assimilation, which limits their adaptability in uncertain and dynamic environments. This paper introduces the active digital twin paradigm, based on active inference. Active inference is a neuroscience-inspired Bayesian framework for probabilistic reasoning and predictive modeling that unifies inference, decision-making, and learning under a single free energy minimization objective. By modeling the dynamics of the coupled physical--digital system as a partially observable Markov decision process, active digital twins autonomously balance pragmatic exploitation (maximizing goal-directed utility) and epistemic exploration (actively resolving uncertainty). As action becomes an integral part of the inference process, active digital twins actively seek information to maintain synchronization with, and learn from their physical counterparts. The proposed framework is assessed through virtual experiments of structural health monitoring and predictive maintenance of a railway bridge. The application showcases the step-by-step construction of a generative model enabling bidirectional perception--action interaction. The results demonstrate that active digital twins exhibit superior exploration capabilities compared to traditional reactive approaches, enabling enhanced autonomy and resilience.

cs.CE↗
arXiv2026

Neural Markov chain Monte Carlo: Bayesian inversion via normalizing flows and variational autoencoders

This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and (ii) are characterized by intractable or unavailable likelihood functions. The posterior probability distribution over quantities of interest is estimated via differential evolution Metropolis sampling, empowered by learnable mappings. First, a variational autoencoder performs probabilistic feature extraction from observational data. The resulting latent structure inherently quantifies uncertainty, capturing deviations between the actual data-generating process and the training data distribution. At each step of the MCMC random walk, the algorithm jointly samples from the data-informed latent distribution and the space of parameters to be inferred. These samples are fed into a neural likelihood estimator based on normalizing flows, specifically real-valued non-volume preserving transformations. The scaling and translation functions of the affine coupling layers are modeled by neural networks conditioned on the unknown parameters, allowing the representation of arbitrary observation likelihoods. The proposed methodology is validated on two case studies: (i) structural health monitoring of a railway bridge for damage detection, localization, and quantification, and (ii) estimation of the conductivity field in a steady-state Darcy's groundwater flow problem. The results demonstrate the efficiency of the inference strategy, while ensuring that model-reality mismatches do not yield overconfident, yet inaccurate, estimates.

cs.CE↗
arXiv2026

HypeRL: Hypernetwork-Based Reinforcement Learning for Control of Parametrized Dynamical Systems

In this work, we devise a new, general-purpose reinforcement learning strategy for the optimal control of parametric dynamical systems. Such problems frequently arise in applied sciences and engineering and entail a significant complexity when control and/or state variables are distributed in high-dimensional space or depend on varying parameters. Traditional numerical methods, relying on either iterative minimization algorithms -- exploiting, e.g., the solution of the adjoint problem -- or dynamic programming -- also involving the solution of the Hamilton-Jacobi-Bellman (HJB) equation -- while reliable, often become computationally infeasible. In this paper, we propose HypeRL a deep reinforcement learning (DRL) framework to overcome the limitations shown by traditional methods. HypeRL aims at approximating the optimal control policy directly. Specifically, we employ an actor-critic DRL approach to learn an optimal feedback control strategy that can generalize across the range of variation of the parameters. To effectively learn such optimal control laws for different instances of the parameters, encoding the parameter information into the DRL policy and value function neural networks (NNs) is essential. HypeRL uses two additional NNs, called hypernetworks, to learn the weights and biases of the value function and the policy NNs. In this way, HypeRL effectively embeds the parametric information into the value function and policy. We validate the proposed approach on two parametric control problems, namely (I) a 1D parametric Kuramoto-Sivashinsky equation with in-domain control, and (ii) a navigation problem of particle dynamics in a parametric 2D gyre flow. We show that the knowledge of physical and task-dependent information and the encoding of this information via a hypernetwork, are essential ingredients for learning parameter-dependent control policies.

cs.LG↗
arXiv2026

Progressive multi-fidelity learning with neural networks for physical system predictions

Highly accurate datasets from numerical or physical experiments are often expensive and time-consuming to acquire, posing a significant challenge for applications that require precise evaluations, potentially across multiple scenarios and in real-time. Even building sufficiently accurate surrogate models can be extremely challenging with limited high-fidelity data. Conversely, less expensive, low-fidelity data can be computed more easily and encompass a broader range of scenarios. By leveraging multi-fidelity information, prediction capabilities of surrogates can be improved. However, in practical situations, data may be different in types, come from sources of different modalities, and not be concurrently available, further complicating the modeling process. To address these challenges, we introduce a progressive multi-fidelity surrogate model. This model can sequentially incorporate diverse data types using tailored encoders. Multi-fidelity regression from the encoded inputs to the target quantities of interest is then performed using neural networks. Input information progressively flows from lower to higher fidelity levels through two sets of connections: concatenations among all the encoded inputs, and additive connections among the final outputs. This dual connection system enables the model to exploit correlations among different datasets while ensuring that each level makes an additive correction to the previous level without altering it. This approach prevents performance degradation as new input data are integrated into the model and automatically adapts predictions based on the available inputs. We demonstrate the effectiveness of the approach on numerical benchmarks and a real-world case study, showing that it reliably integrates multi-modal data and provides accurate predictions, maintaining performance when generalizing across time and parameter variations.

cs.LG↗
arXiv2025

Multi-Fidelity Delayed Acceptance: hierarchical MCMC sampling for Bayesian inverse problems combining multiple solvers through deep neural networks

Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial differential equations are involved, full-order models such as those based on the Finite Element Method can make traditional sampling approaches like Markov Chain Monte Carlo (MCMC) computationally infeasible. Although data-driven surrogate models may help reduce evaluation costs, their utility is often limited by the expense of generating high-fidelity data. In contrast, low-fidelity data can be produced more efficiently, although relying on them alone may degrade the accuracy of the inverse UQ solution. To address these challenges, we propose a Multi-Fidelity Delayed Acceptance scheme for Bayesian inverse problems. Extending the Multi-Level Delayed Acceptance framework, the method introduces multi-fidelity neural networks that combine the predictions of solvers of varying fidelity, with high fidelity evaluations restricted to an offline training stage. During the online phase, likelihood evaluations are obtained by evaluating the coarse solvers and passing their outputs to the trained neural networks, thereby avoiding additional high-fidelity simulations. This construction allows heterogeneous coarse solvers to be incorporated consistently within the hierarchy, providing greater flexibility than standard Multi-Level Delayed Acceptance. The proposed approach improves the approximation accuracy of the low fidelity solvers, leading to longer sub-chain lengths, better mixing, and accelerated posterior inference. The effectiveness of the strategy is demonstrated on two benchmark inverse problems involving (i) steady isotropic groundwater flow, (ii) an unsteady reaction-diffusion system, for which substantial computational savings are obtained.

cs.LG↗
arXiv2025

Adaptive digital twins for predictive decision-making: Online Bayesian learning of transition dynamics

This work shows how adaptivity can enhance value realization of digital twins in civil engineering. We focus on adapting the state transition models within digital twins represented through probabilistic graphical models. The bi-directional interaction between the physical and virtual domains is modeled using dynamic Bayesian networks. By treating state transition probabilities as random variables endowed with conjugate priors, we enable hierarchical online learning of transition dynamics from a state to another through effortless Bayesian updates. We provide the mathematical framework to account for a larger class of distributions with respect to the current literature on digital twins. To compute dynamic policies with precision updates we solve parametric Markov decision processes through reinforcement learning. The proposed adaptive digital twin framework enjoys enhanced personalization, increased robustness, and improved cost-effectiveness. We assess our approach on a case study involving structural health monitoring and maintenance planning of a railway bridge.

cs.LG↗
arXiv2025

VENI, VINDy, VICI: a generative reduced-order modeling framework with uncertainty quantification

The simulation of many complex phenomena in engineering and science requires solving expensive, high-dimensional systems of partial differential equations (PDEs). To circumvent this, reduced-order models (ROMs) have been developed to speed up computations. However, when governing equations are unknown or partially known, typically ROMs lack interpretability and reliability of the predicted solutions. In this work we present a data-driven, non-intrusive framework for building ROMs where the latent variables and dynamics are identified in an interpretable manner and uncertainty is quantified. Starting from a limited amount of high-dimensional, noisy data the proposed framework constructs an efficient ROM by leveraging variational autoencoders for dimensionality reduction along with a newly introduced, variational version of sparse identification of nonlinear dynamics (SINDy), which we refer to as Variational Identification of Nonlinear Dynamics (VINDy). In detail, the method consists of Variational Encoding of Noisy Inputs (VENI) to identify the distribution of reduced coordinates. Simultaneously, we learn the distribution of the coefficients of a pre-determined set of candidate functions by VINDy. Once trained offline, the identified model can be queried for new parameter instances and new initial conditions to compute the corresponding full-time solutions. The probabilistic setup enables uncertainty quantification as the online testing consists of Variational Inference naturally providing Certainty Intervals (VICI). In this work we showcase the effectiveness of the newly proposed VINDy method in identifying interpretable and accurate dynamical system for the Roessler system with different noise intensities and sources. Then the performance of the overall method - named VENI, VINDy, VICI - is tested on PDE benchmarks including structural mechanics and fluid dynamics.

cs.LG↗
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

Enhancing Bayesian model updating in structural health monitoring via learnable mappings

In the context of structural health monitoring (SHM), the selection and extraction of damage-sensitive features from raw sensor recordings represent a critical step towards solving the inverse problem underlying the identification of structural health conditions. This work introduces a novel approach that employs deep neural networks to enhance stochastic SHM methods. A learnable feature extractor and a feature-oriented surrogate model are synergistically exploited to evaluate a likelihood function within a Markov chain Monte Carlo sampling algorithm. The feature extractor undergoes pairwise supervised training to map sensor recordings onto a low-dimensional metric space, which encapsulates the sensitivity to structural health parameters. The surrogate model maps structural health parameters to their feature representation. The procedure enables the updating of beliefs about structural health parameters, eliminating the need for computationally expensive numerical models. A preliminary offline phase involves the generation of a labeled dataset to train both the feature extractor and the surrogate model. Within a simulation-based SHM framework, training vibration responses are efficiently generated using a multi-fidelity surrogate modeling strategy to approximate sensor recordings under varying damage and operational conditions. The multi-fidelity surrogate exploits model order reduction and artificial neural networks to speed up the data generation phase while ensuring the damage-sensitivity of the approximated signals. The proposed strategy is assessed through three synthetic case studies, demonstrating high accuracy in the estimated parameters and strong computational efficiency.

cs.CE↗
arXiv2025

Reduced Order Modeling with Shallow Recurrent Decoder Networks

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control. However, conventional dimensionality reduction techniques are typically limited to known and constant parameters, inefficient for nonlinear and chaotic dynamics, and uninformed to the actual system behavior. In this work, we propose sensor-driven SHallow REcurrent Decoder networks for Reduced Order Modeling (SHRED-ROM). Specifically, we consider the composition of a long short-term memory network, which encodes the temporal dynamics of limited sensor data in multiple scenarios, and a shallow decoder, which reconstructs the corresponding high-dimensional states. SHRED-ROM is a robust decoding-only strategy that circumvents the numerically unstable approximation of an inverse which is required by encoding-decoding schemes. To enhance computational efficiency and memory usage, the full-order state snapshots are reduced by, e.g., proper orthogonal decomposition, allowing for compressive training of the networks with minimal hyperparameter tuning. Through applications on chaotic and nonlinear fluid dynamics, we show that SHRED-ROM (i) accurately reconstructs the state dynamics for new parameter values starting from limited fixed or mobile sensors, independently on sensor placement, (ii) can cope with both physical, geometrical and time-dependent parametric dependencies, while being agnostic to their actual values, (iii) can accurately estimate unknown parameters, and (iv) can deal with different data sources, such as high-fidelity simulations, coupled fields and videos.

cs.LG↗
arXiv2024

On latent dynamics learning in nonlinear reduced order modeling

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality reduction problem, while constraining the latent state to evolve accordingly to an (unknown) dynamical system. A time-continuous setting is employed to derive error and stability estimates for the LDM approximation of the full order model (FOM) solution. We analyze the impact of using an explicit Runge-Kutta scheme in the time-discrete setting, resulting in the $Δ\text{LDM}$ formulation, and further explore the learnable setting, $Δ\text{LDM}_θ$, where deep neural networks approximate the discrete LDM components, while providing a bounded approximation error with respect to the FOM. Moreover, we extend the concept of parameterized Neural ODE - recently proposed as a possible way to build data-driven dynamical systems with varying input parameters - to be a convolutional architecture, where the input parameters information is injected by means of an affine modulation mechanism, while designing a convolutional autoencoder neural network able to retain spatial-coherence, thus enhancing interpretability at the latent level. Numerical experiments, including the Burgers' and the advection-reaction-diffusion equations, demonstrate the framework's ability to obtain, in a multi-query context, a time-continuous approximation of the FOM solution, thus being able to query the LDM approximation at any given time instance while retaining a prescribed level of accuracy. Our findings highlight the remarkable potential of the proposed LDMs, representing a mathematically rigorous framework to enhance the accuracy and approximation capabilities of reduced order modeling for time-dependent parameterized PDEs.

math.NA↗