arXiv subjects

Harsha Vardhan Tetali

Publications and source records attributed to Harsha Vardhan Tetali.

6 recordsLinked to original sources

arXiv2026

Neural Surrogate Modeling of Ultrasonic Wave Propagation in Heterogeneous Media

Neural surrogates provide computationally efficient auto-regressive modeling of wave propagation, enabling e.g. fast inverse solutions. Despite recent progress, the current surrogates are not yet sufficient for the needs of ultrasonic sensing, characterized by high frequency and heterogeneous propagation media. We show how methods building on Fourier Neural Operators (FNO) fail to capture essential signal features, such as reflections, whereas U-Net -based methods learn the wave fields well but lack the ability to transfer information across different spatial scales. We then propose a new surrogate that captures the best of the two worlds, by integrating FNOs and local-integral resampling into a U-Net architecture. We show it can be trained on limited data, and that the predictions are robust to input noise and work across spatial scales.

cs.LG↗

arXiv2026

Spatial Thickness Mapping in Heterogeneous Plate Using Wave Physics-Informed Regression

Traditional guided wave methods for structural health monitoring typically assume uniform material properties, which limit their ability to characterize heterogeneous structures with spatially varying thickness, damage, or material properties. These are challenges commonly encountered in corrosion assessment, composite delamination detection, and structural degradation monitoring. This paper presents a wave physics-informed regression approach that enables spatially resolved characterization of material properties by extracting local dispersion curves across a structure. Our approach focuses on a highly interpretable but flexible physics-informed framework that can be solved using fast algorithms and achieve robust numerical solutions. This paper discusses the mathematical design of the framework, the algorithm, and its interpretation. The framework was applied to a guided wave wavefield imaging dataset from a thin aluminum plate with non-uniform thickness around a hole to validate its practicality. The framework creates an accurate thickness map (correlation coefficient 0.94 with x-ray CT validation) as well as extracts the frequency-dependent velocities of waves within those regions.

eess.SP↗

arXiv2026

Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification

We propose a conjugate and calibrated Gaussian process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained Euclidean representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.

cs.LG↗

arXiv2023

Wave Physics-informed Matrix Factorizations

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it {nearly} satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality. Through this line of work we establish theoretical connections between wave-informed learning and filtering theory in signal processing. We further demonstrate the application of this work on modal analysis problems commonly arising in structural diagnostics and prognostics.

cs.LG↗

arXiv2023

On the Generalization Error of Meta Learning for the Gibbs Algorithm

We analyze the generalization ability of joint-training meta learning algorithms via the Gibbs algorithm. Our exact characterization of the expected meta generalization error for the meta Gibbs algorithm is based on symmetrized KL information, which measures the dependence between all meta-training datasets and the output parameters, including task-specific and meta parameters. Additionally, we derive an exact characterization of the meta generalization error for the super-task Gibbs algorithm, in terms of conditional symmetrized KL information within the super-sample and super-task framework introduced in Steinke and Zakynthinou (2020) and Hellstrom and Durisi (2022) respectively. Our results also enable us to provide novel distribution-free generalization error upper bounds for these Gibbs algorithms applicable to meta learning.

cs.LG↗

arXiv2021

Wave-Informed Matrix Factorization with Global Optimality Guarantees

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality in polynomial time. We demonstrate the benefits of our work by applications in structural health monitoring, where prior work has attempted to solve this problem using sparse dictionary learning approaches that do not come with any theoretical guarantees regarding convergence to global optimality and employ heuristics to capture desired physical constraints.

cs.LG↗