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].

In one view, this theorem extends the universality of "complete-observation" GNNs in to "partial-observation".

Traditional neural networks, while powerful, rely on biologically implausible learning mechanisms such as global backpropagation. This paper introduces the Structurally Adaptive Predictive Inference Network (SAPIN), a novel computational model inspired by the principles of active inference and the morphological plasticity observed in biological neural cultures. SAPIN operates on a 2D grid where processing units, or cells, learn by minimizing local prediction errors. The model features two primary, concurrent learning mechanisms: a local, Hebbian-like synaptic plasticity rule based on the temporal difference between a cell's actual activation and its learned expectation, and a structural plasticity mechanism where cells physically migrate across the grid to optimize their information-receptive fields. This dual approach allows the network to learn both how to process information (synaptic weights) and also where to position its computational resources (network topology). We validated the SAPIN model on the classic Cart Pole reinforcement learning benchmark. Our results demonstrate that the architecture can successfully solve the CartPole task, achieving robust performance. The network's intrinsic drive to minimize prediction error and maintain homeostasis was sufficient to discover a stable balancing policy. We also found that while continual learning led to instability, locking the network's parameters after achieving success resulted in a stable policy. When evaluated for 100 episodes post-locking (repeated over 100 successful agents), the locked networks maintained an average 82% success rate.

The Cheap Gradient Principle [Griewank and Walther, 2008] -- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of 5) as that of simply computing the function itself -- is of central importance in optimization; it allows us to quickly obtain (high dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures. The current state of affairs is markedly different with regards to computing subderivatives: widely used ML libraries, including TensorFlow and PyTorch, do not correctly compute (generalized) subderivatives even on simple examples. This work considers the question: is there a Cheap Subgradient Principle? Our main result shows that, under certain restrictions on our library of nonsmooth functions (standard in nonlinear programming), provably correct generalized subderivatives can be computed at a computational cost that is within a (dimension-free) factor of 6 of the cost of computing the scalar function itself.

The Cheap Gradient Principle [Griewank and Walther, 2008] -- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of 5) as that of simply computing the function itself -- is of central importance in optimization; it allows us to quickly obtain (high dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based optimization procedures. The current state of affairs is markedly different with regards to computing subderivatives: widely used ML libraries, including TensorFlow and PyTorch, do not correctly compute (generalized) subderivatives even on simple examples. This work considers the question: is there a Cheap Subgradient Principle? Our main result shows that, under certain restrictions on our library of nonsmooth functions (standard in nonlinear programming), provably correct generalized subderivatives can be computed at a computational cost that is within a (dimension-free) factor of 6 of the cost of computing the scalar function itself.

Mean correlation values across the synchronous, (i.e., stimulus-driven) cortex defined at a range of synchrony thresholds ([0.15,0.75]). We employed the HCP MMP parcellation for all ROI-level analysis. Figure 3 depicts the center-weighted saliency map used in all center-weighted attention models. Thus, the output is a 160900-D vector corresponding to the fMRI response. FDR corrected) for each method are colored on the surface.

Thus, there is a need for a reference point, on which each model can be tested and from where potential improvements can be derived. In this study, we select publicly available state-of-the-art visual search models and datasets in natural scenes, and provide a common framework for their evaluation. To this end, we apply a unified format and criteria, bridging the gaps between them, and we estimate the models' efficiency and similarity with humans using a specific set of metrics.

The empirically established null subject (NS) stage, lasting until about 4 years of age, involves frequent omission of subjects by children. Orfitelli and Hyams (2012) observe that young English speakers often confuse imperative NS utterances with declarative ones due to performance influences, promoting a temporary null subject grammar. We propose a new computational parameter to measure this misinterpretation and incorporate it into a simulated model of obligatory subject grammar learning. Using a modified version of the Variational Learner (Yang, 2012) which works for superset-subset languages, our simulations support Orfitelli and Hyams' hypothesis. More generally, this study outlines a framework for integrating computational models in the study of grammatical acquisition alongside other key developmental factors.

Cognitive science faces ongoing challenges in knowledge synthesis and conceptual clarity, in part due to its multifaceted and interdisciplinary nature. Recent advances in artificial intelligence, particularly the development of large language models (LLMs), offer tools that may help to address these issues. This review examines how LLMs can support areas where the field has historically struggled, including establishing cross-disciplinary connections, formalizing theories, developing clear measurement taxonomies, achieving generalizability through integrated modeling frameworks, and capturing contextual and individual variation. We outline the current capabilities and limitations of LLMs in these domains, including potential pitfalls. Taken together, we conclude that LLMs can serve as tools for a more integrative and cumulative cognitive science when used judiciously to complement, rather than replace, human expertise.