State-space models provide a powerful framework for describing the evolution of hidden states in dynamical systems [3], [4], [1]. Conventionally, state-space models assume Gaussian measurement and state noise, owing to their tractability and well-characterized statistical properties. However, many real-world phenomena are subject to perturbations that deviate from the conventional Gaussian noise assumption. In radio interferometry, for instance, observational data are frequently corrupted by non-Gaussian noise sources such as radio-frequency interference (RFI) [5], [2], which originates from man-made signals and introduces significant distortions into astronomical measurements [6], [30]. Such interference produces sporadic high-power spikes in the measured visibilities, leading to heavy-tailed statistics. Many radio-interferometric reconstruction methods assume Gaussian additive noise [7], [31], [33], [35], an approximation that can lead to inaccurate reconstructions when the heavy-tailed nature of real-world measurement noise is not properly accounted for. In the realm of state-space modeling, addressing non-Gaussian noise has led to the development of various methodological approaches, notably particle filtering and non-conventional Kalman filters. Particle filters [8], or Sequential Monte Carlo methods, are designed to handle non-linear and non-Gaussian state-space models by representing the posterior distribution with a set of weighted samples [9], [10], [32].

Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a library of candidate functions. Therefore, it relies on the assumption that the dynamics are sparsely represented in the coordinate system used. To address this limitation, one seeks a coordinate transformation that provides reduced coordinates capable of reconstructing the original system. Recently, SINDy autoencoders have extended this idea by combining sparse model discovery with autoencoder architectures to learn simplified latent coordinates together with parsimonious governing equations. A central challenge in this framework is robustness to measurement error. Inspired by noise-separating neural network structures, we incorporate a noise-separation module into the SINDy autoencoder architecture, thereby improving robustness and enabling more reliable identification of noisy dynamical systems. Numerical experiments on the Lorenz system show that the proposed method recovers interpretable latent dynamics and accurately estimates the measurement noise from noisy observations.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

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].

We present a neural network-based framework for solving the quantitative group testing (QGT) problem that achieves both high decoding accuracy and structural verifiability. In QGT, the objective is to identify a small subset of defective items among $N$ candidates using only $M \ll N$ pooled tests, each reporting the number of defectives in the tested subset. We train a multi-layer perceptron to map noisy measurement vectors to binary defect indicators, achieving accurate and robust recovery even under sparse, bounded perturbations. Beyond accuracy, we show that the trained network implicitly learns the underlying pooling structure that links items to tests, allowing this structure to be recovered directly from the network's Jacobian. This indicates that the model does not merely memorize training patterns but internalizes the true combinatorial relationships governing QGT. Our findings reveal that standard feedforward architectures can learn verifiable inverse mappings in structured combinatorial recovery problems.

This paper introduces a novel Kalman filter framework designed to achieve robust state estimation under both process and measurement noise. Inspired by the Weighted Observation Likelihood Filter (WoLF), which provides robustness against measurement outliers, we applied generalized Bayesian approach to build a framework considering both process and measurement noise outliers.

V alid causal inference in observational studies often requires controlling for con-founders.

This work was undertaken whilst AS was a Visiting Research Fellow with University of Cambridge.