arXiv:2603.13806v1 Announce Type: new Abstract: Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on variables and does not account for differences in variable importance, which may lead to unstable performance in highly noisy or structurally complex settings. We propose SP-SPCA, a method that introduces a single equilibrium parameter into the regularization framework to adaptively adjust variable penalties. This […]

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Deep learning (DL) models have achieved strong performance in an intelligence healthcare setting, yet most existing approaches operate as black boxes and ignore the physical processes that govern tumor growth, limiting interpretability, robustness, and clinical trust. To address this limitation, we propose PhysNet, a physics-embedded DL framework that integrates tumor growth dynamics directly into the feature learning process of a convolutional neural network (CNN). Unlike conventional physics-informed methods that impose physical constraints only at the output level, PhysNet […]

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Hi all, I’m training a quadruped robot (Isaac Gym / legged_gym style) and trying to achieve a policy that switches between: – command = 0 → stable quadruped standing – command = 1 → stable bipedal standing (hind legs only) However, I’m facing several issues that seem related to reward scaling and interference between reward terms. Current reward components: – zero linear/angular velocity tracking – projected gravity alignment – quadruped base height reward – bipedal base height reward […]

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Accurately quantifying uncertainty in predictions and projections arising from irreducible internal climate variability is critical for informed decision making. Such uncertainty is typically assessed using ensembles produced with physics based climate models. However, computational constraints impose a trade off between generating the large ensembles required for robust uncertainty estimation and increasing model resolution to better capture fine scale dynamics. Generative machine learning offers a promising pathway to alleviate these constraints. We develop a conditional Variational Autoencoder (cVAE) trained […]

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Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit spectral bias, whereby low-frequency components of the solution are learned significantly faster than high-frequency modes. While spectral bias is often treated as an intrinsic representational limitation of neural architectures, its interaction with optimization dynamics and physics-based loss formulations remains poorly understood. In this work, we provide a systematic investigation […]

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Deep reinforcement learning (RL) has been applied extensively to solve complex decision-making problems. In many real-world scenarios, tasks often have several conflicting objectives and may require multiple agents to cooperate, which are the multi-objective multi-agent decision-making problems. However, only few works have been conducted on this intersection. Existing approaches are limited to separate fields and can only handle multi-agent decision-making with a single objective, or multi-objective decision-making with a single agent. In this paper, we propose MO-MIX to […]

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Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing some promise. However, in contrast to model-driven algorithms, analysis of these data-driven methods is poorly developed. In this paper we address this issue, developing a theory to underpin data-driven methods to solve smoothing problems arising in data assimilation and forecasting problems. The theoretical framework relies on two key components: (i) establishing the existence […]

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arXiv:2603.28917v1 Announce Type: cross Abstract: This work uncovers variational principles behind symmetrizing the Bregman divergences induced by generic mirror maps over the cone of positive definite matrices. We show that computing the canonical means for this symmetrization can be posed as minimizing the desired symmetrized divergences over a set of mean functionals defined axiomatically to satisfy certain properties. For the forward symmetrization, we prove that the arithmetic mean over the primal space is canonical for any mirror map […]

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