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This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the…
Disruption prediction has made rapid progress in recent years, especially in machine learning (ML)-based methods. Understanding why a predictor makes a certain prediction can be as crucial as the prediction's accuracy for future tokamak…
Many recent language model (LM) interpretability studies have adopted the circuits framework, which aims to find the minimal computational subgraph, or circuit, that explains LM behavior on a given task. Most studies determine which edges…
Spectral projectors and the reflectors derived from them are basic objects in numerical linear algebra. This paper studies the prescribed-index reflector I-2P_k, where P_k is the spectral projector associated with the first k eigenvectors…
We present a novel subset scan method to detect if a probabilistic binary classifier has statistically significant bias -- over or under predicting the risk -- for some subgroup, and identify the characteristics of this subgroup. This form…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly,…
Uncertainty estimation has been widely studied in medical image segmentation as a tool to provide reliability, particularly in deep learning approaches. However, previous methods generally lack effective supervision in uncertainty…
Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular…
Interpretability is often an essential requirement in medical imaging. Advanced deep learning methods are required to address this need for explainability and high performance. In this work, we investigate whether additional information…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
Speeded Up Robust Features (SURF) has emerged as one of the more popular feature descriptors and detectors in recent years. Performance and algorithmic details vary widely between implementations due to SURF's complexity and ambiguities…
Pseudospectral schemes are a class of numerical methods capable of solving smooth problems with high accuracy thanks to their exponential convergence to the true solution. When applied to discontinuous problems, such as fluid shocks and…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated with parametric…
Forecasting multiscale chaotic dynamical systems, such as turbulent flows, with deep learning remains a formidable challenge due to the spectral bias of neural networks, which hinders the accurate representation of fine-scale structures in…
Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equations, several approaches have been developed to quantify the…
Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard…
Sewer pipe faults, such as leaks and blockages, can lead to severe consequences including groundwater contamination, property damage, and service disruption. Traditional inspection methods rely heavily on the manual review of CCTV footage…
The transformation of conventional power networks into smart grids with the heavy penetration level of renewable energy resources, particularly grid-connected Photovoltaic (PV) systems, has increased the need for efficient fault…