Machine learning assisted state prediction of misspecified linear dynamical system via modal reduction Rohan Vittal Thorat a, Rajdip Nayek a a Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi, 110016, IndiaAbstract Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in geometry, material behavior, damping, or boundary conditions, resulting in model form errors (MFEs) that impair predictive accuracy. This work introduces a comprehensive framework for MFE estimation and correction in high-dimensional finite element (FE) based structural dynamical systems. The Gaussian Process Latent Force Model (GPLFM) represents discrepancies non-parametrically in the reduced modal domain, allowing a flexible data-driven characterization of unmodeled dynamics. A linear Bayesian filtering approach jointly estimates system states and discrepancies, incorporating epistemic and aleatoric uncertainties. To ensure computational tractability, the FE system is projected onto a reduced modal basis, and a mesh-invariant neural network maps modal states to discrepancy estimates, permitting model rectification across different FE dis-cretizations without retraining. Validation is undertaken across five MFE scenarios--including incorrect beam theory, damping misspecification, misspecified boundary condition, unmodeled material nonlinearity, and local damage --demonstrating the surrogate model's substantial reduction of displacement and rotation prediction errors under unseen excitations. The proposed methodology offers a potential means to uphold digital twin accuracy amid inherent modeling uncertainties. Keywords: Model bias, Gaussian Process, Latent Force Model, Bayesian filtering, Modal reduction, Digital twin 1. Introduction The reliable simulation of structural dynamical systems is central to engineering analysis, design, and decision-making. In practice, high-fidelity models are often impractical due to limited information, computational constraints, or simplifying assumptions in geometry, boundary conditions, damping mechanisms, and material constitutive laws. These idealizations lead to model form errors (MFEs)--systematic discrepancies between the predicted and actual system responses--which, if unaccounted for, can significantly degrade predictive accuracy. This challenge is especially critical in the context of digital twins, where model predictions directly inform monitoring and decision-making. Digital twins of structural systems integrate computational models with real-time or historical measurement data to enable continuous prediction, monitoring, and decision making [1, 2].

This work presents a probabilistic digital twin framework for response prediction in dynamical systems governed by misspecified physics. The approach integrates Gaussian Process Latent Force Models (GPLFM) and Bayesian Neural Networks (BNNs) to enable end-to-end uncertainty-aware inference and prediction. In the diagnosis phase, model-form errors (MFEs) are treated as latent input forces to a nominal linear dynamical system and jointly estimated with system states using GPLFM from sensor measurements. A BNN is then trained on posterior samples to learn a probabilistic nonlinear mapping from system states to MFEs, while capturing diagnostic uncertainty. For prognosis, this mapping is used to generate pseudo-measurements, enabling state prediction via Kalman filtering. The framework allows for systematic propagation of uncertainty from diagnosis to prediction, a key capability for trustworthy digital twins. The framework is demonstrated using four nonlinear examples: a single degree of freedom (DOF) oscillator, a multi-DOF system, and two established benchmarks -- the Bouc-Wen hysteretic system and the Silverbox experimental dataset -- highlighting its predictive accuracy and robustness to model misspecification.

Real-time sea state estimation is vital for applications like shipbuilding and maritime safety. Traditional methods rely on accurate wave-vessel transfer functions to estimate wave spectra from onboard sensors. In contrast, our approach jointly estimates sea state and vessel parameters without needing prior transfer function knowledge, which may be unavailable or variable. We model the wave-vessel system using pseudo mass-spring-dampers and develop a dynamic model for the system. This method allows for recursive modeling of wave excitation as a time-varying input, relaxing prior works' assumption of a constant input. We derive statistically consistent process noise covariance and implement a square root cubature Kalman filter for sensor data fusion. Further, we derive the Posterior Cramer-Rao lower bound to evaluate estimator performance. Extensive Monte Carlo simulations and data from a high-fidelity validated simulator confirm that the estimated wave spectrum matches methods assuming complete transfer function knowledge.

We consider the adaptive control problem for discrete-time, nonlinear stochastic systems with linearly parameterised uncertainty. Assuming access to a parameterised family of controllers that can stabilise the system in a bounded set within an informative region of the state space when the parameter is well-chosen, we propose a certainty equivalence learning-based adaptive control strategy, and subsequently derive stability bounds on the closed-loop system that hold for some probabilities. We then show that if the entire state space is informative, and the family of controllers is globally stabilising with appropriately chosen parameters, high probability stability guarantees can be derived.

In particular, in Appendix E.1 we show the Table 2 provides the notations used throughout the paper. The precise expressions are given throughout the Appendix in stated sections. In this section, we provide the proof of Theorem 1 with precise expressions. Combining (26) and (27) gives the self-normalized estimation error bound state in the theorem.D.2 Frobenius Norm Bound on Finite Sample Estimation Error of (10) Using this result, we have σ It represents the effect of noises in the system on the outputs. E.1 Persistence of Excitation in Warm-up Recall the state-space form of the system, x Using Weyl's inequality, during the warm-up period with probability 1 δ, we have σ Now consider when the underlying system is known.

We thank the reviewers for their effort and insightful comments during these unprecedented times. LQR & LQG are among few continuous settings where the optimal policies exist (and mainly have closed form) [1]. Therefore, we do not see why this paper would be less relevant to our community. If PE is absent, we provide two general algorithms stated in Cor. The agent uses a warm-up period of O ( T) after which it commits to a controller yielding a regret of T .

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Acoustic sensors, particularly Doppler V elocity Logs (DVLs), have become indispensable for underwater navigation and environmental sensing. To enable robust fusion of DVL measurements with data from other sensors, precise calibration of extrinsic parameters and temporal synchronization is critical, especially in challenging underwater operating conditions [1]-[5]. Prior work by Xu et al. [6] and Westman and Kaes [7] framed the DVL-camera calibration as an odometry alignment problem, matching the trajectory from a DVL-IMU system against the visual one from a camera. A critical limitation of these approaches is their implicit assumption of known and static DVL-IMU extrinsics, which is frequently violated in underwater environments due to their dynamic nature. While studies in [8]-[11] address the calibration of IMU-free DVLs, their applicability is strictly limited to co-sensors that provide direct linear and angular velocity measurements, such as SINS/GPS systems. Crucially, a significant gap persists across all these works: none address the calibration of translational extrinsic nor account for temporal synchronization across heterogeneous sensors.

Abstract--This study investigates the behavior of Causal Con-volutional Neural Networks (CNNs) with quasi-linear activation functions when applied to time-series data characterized by mul-timodal frequency content. We demonstrate that, once trained, such networks exhibit properties analogous to Finite Impulse Response (FIR) filters, particularly when the convolutional kernels are of extended length exceeding those typically employed in standard CNN architectures. Causal CNNs are shown to capture spectral features both implicitly and explicitly, offering enhanced interpretability for tasks involving dynamic systems. Leveraging the associative property of convolution, we further show that the entire network can be reduced to an equivalent single-layer filter resembling an FIR filter optimized via least-squares criteria. This equivalence yields new insights into the spectral learning behavior of CNNs trained on signals with sparse frequency content. The approach is validated on both simulated beam dynamics and real-world bridge vibration datasets, underlining its relevance for modeling and identifying physical systems governed by dynamic responses. Neural networks have enjoyed wide-spread adoption across various modeling tasks, despite the common pitfall of typically comprising black box models that are often difficult to interpret [1]. It is therefore challenging to tailor a neural network model according to the characteristics of a specific problem: how can we introduce a bias inside a black box? A common way to introduce biases is through the architecture of the neural network. For example, Convolution Neural Networks employ convolutional kernels to force the network to focus on local correlations, which is different from the global connectivity of Multi-Layer Perceptrons. This bias is useful for image processing tasks, where the information of a single pixel is highly correlated with its surrounding pixels [2]. For physics-informed neural networks [3], the bias to be introduced should reflect the prior knowledge on the physical laws that govern the phenomenon that the model is trying to replicate. Due to the black box nature of neural networks, such biases need to be implemented explicitly, e.g. with a physics-informed loss function, rather than an implicit bias in the architecture of the model. In the case of the dynamical behavior of physical systems, a desirable bias should capture the dynamic properties of a system.

Deep learning-based gait recognition has achieved great success in various applications. The key to accurate gait recognition lies in considering the unique and diverse behavior patterns in different motion regions, especially when covariates affect visual appearance. However, existing methods typically use predefined regions for temporal modeling, with fixed or equivalent temporal scales assigned to different types of regions, which makes it difficult to model motion regions that change dynamically over time and adapt to their specific patterns. To tackle this problem, we introduce a Region-aware Dynamic Aggregation and Excitation framework (GaitRDAE) that automatically searches for motion regions, assigns adaptive temporal scales and applies corresponding attention. Specifically, the framework includes two core modules: the Region-aware Dynamic Aggregation (RDA) module, which dynamically searches the optimal temporal receptive field for each region, and the Region-aware Dynamic Excitation (RDE) module, which emphasizes the learning of motion regions containing more stable behavior patterns while suppressing attention to static regions that are more susceptible to covariates. Experimental results show that GaitRDAE achieves state-of-the-art performance on several benchmark datasets.