Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineering. The Sindy algorithm has proven effective in leveraging sparsity to identify concise models of nonlinear dynamical systems. In this paper, we extend sparsity-driven approaches to real-time learning by integrating a cornerstone algorithm from control theory -- the Kalman filter (KF). The resulting Sindy Kalman Filter (SKF) unifies both frameworks by treating unknown system parameters as state variables, enabling real-time inference of complex, time-varying nonlinear models unattainable by either method alone. Furthermore, SKF enhances KF parameter identification strategies, particularly via look-ahead error, significantly simplifying the estimation of sparsity levels, variance parameters, and switching instants. We validate SKF on a chaotic Lorenz system with drifting or switching parameters and demonstrate its effectiveness in the real-time identification of a sparse nonlinear aircraft model built from real flight data.

This paper addresses the critical challenge of improving predictions of climate extreme events, specifically heat waves, using machine learning methods. Our work is framed as a classification problem in which we try to predict whether surface air temperature will exceed its q-th local quantile within a specified timeframe. Our key finding is that aggregating ensemble predictions using a power mean significantly enhances the classifier's performance. By making a machine-learning based weather forecasting model generative and applying this non-linear aggregation method, we achieve better accuracy in predicting extreme heat events than with the typical mean prediction from the same model. Our power aggregation method shows promise and adaptability, as its optimal performance varies with the quantile threshold chosen, demonstrating increased effectiveness for higher extremes prediction.

In the context of Visual Question Answering (VQA) and Agentic AI, calibration refers to how closely an AI system's confidence in its answers reflects their actual correctness. This aspect becomes especially important when such systems operate autonomously and must make decisions under visual uncertainty. While modern VQA systems, powered by advanced vision-language models (VLMs), are increasingly used in high-stakes domains like medical diagnostics and autonomous navigation due to their improved accuracy, the reliability of their confidence estimates remains under-examined. Particularly, these systems often produce overconfident responses. To address this, we introduce AlignVQA, a debate-based multi-agent framework, in which diverse specialized VLM -- each following distinct prompting strategies -- generate candidate answers and then engage in two-stage interaction: generalist agents critique, refine and aggregate these proposals. This debate process yields confidence estimates that more accurately reflect the model's true predictive performance. We find that more calibrated specialized agents produce better aligned confidences. Furthermore, we introduce a novel differentiable calibration-aware loss function called aligncal designed to fine-tune the specialized agents by minimizing an upper bound on the calibration error. This objective explicitly improves the fidelity of each agent's confidence estimates. Empirical results across multiple benchmark VQA datasets substantiate the efficacy of our approach, demonstrating substantial reductions in calibration discrepancies. Furthermore, we propose a novel differentiable calibration-aware loss to fine-tune the specialized agents and improve the quality of their individual confidence estimates based on minimising upper bound calibration error.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

The Dual Diffusion Implicit Bridge (DDIB) is an emerging image-to-image (I2I) translation method that preserves cycle consistency while achieving strong flexibility. It links two independently trained diffusion models (DMs) in the source and target domains by first adding noise to a source image to obtain a latent code, then denoising it in the target domain to generate the translated image. However, this method faces two key challenges: (1) low translation efficiency, and (2) translation trajectory deviations caused by mismatched latent distributions. To address these issues, we propose a novel I2I translation framework, OT-ALD, grounded in optimal transport (OT) theory, which retains the strengths of DDIB-based approach. Specifically, we compute an OT map from the latent distribution of the source domain to that of the target domain, and use the mapped distribution as the starting point for the reverse diffusion process in the target domain. Our error analysis confirms that OT-ALD eliminates latent distribution mismatches. Moreover, OT-ALD effectively balances faster image translation with improved image quality. Experiments on four translation tasks across three high-resolution datasets show that OT-ALD improves sampling efficiency by 20.29% and reduces the FID score by 2.6 on average compared to the top-performing baseline models.

Deep learning models for precipitation forecasting often function as black boxes, limiting their adoption in real-world weather prediction. To enhance transparency while maintaining accuracy, we developed an interpretable deep learning framework for short-term precipitation prediction in four major Indian cities: Bengaluru, Mumbai, Delhi, and Kolkata, spanning diverse climate zones. We implemented a hybrid Time-Distributed CNN-ConvLSTM (Convolutional Neural Network-Long Short-Term Memory) architecture, trained on multi-decadal ERA5 reanalysis data. The architecture was optimized for each city with a different number of convolutional filters: Bengaluru (32), Mumbai and Delhi (64), and Kolkata (128). The models achieved root mean square error (RMSE) values of 0.21 mm/day (Bengaluru), 0.52 mm/day (Mumbai), 0.48 mm/day (Delhi), and 1.80 mm/day (Kolkata). Through interpretability analysis using permutation importance, Gradient-weighted Class Activation Mapping (Grad-CAM), temporal occlusion, and counterfactual perturbation, we identified distinct patterns in the model's behavior. The model relied on city-specific variables, with prediction horizons ranging from one day for Bengaluru to five days for Kolkata. This study demonstrates how explainable AI (xAI) can provide accurate forecasts and transparent insights into precipitation patterns in diverse urban environments.

We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are decomposed into a sequence of linear subproblems, which are efficiently solved using a Multi-Head PINN. Once the latent representation of the linear operator is learned, solutions to new PDE instances with varying perturbations, forcing terms, or boundary/initial conditions can be obtained in closed form without retraining. We validate the method on KPP-Fisher and wave equations, achieving errors on the order of 1e-3 while adapting to new problem instances in under 0.2 seconds; comparable accuracy to classical solvers but with faster transfer. Sensitivity analyses show predictable error growth with epsilon and polynomial degree, clarifying the method's effective regime. Our contributions are: (i) extending one-shot transfer learning from nonlinear ODEs to PDEs, (ii) deriving a closed-form solution for adapting to new PDE instances, and (iii) demonstrating accuracy and efficiency on canonical nonlinear PDEs. We conclude by outlining extensions to derivative-dependent nonlinearities and higher-dimensional PDEs.

How to best use Large Language Models (LLMs) for software engineering is covered in many publications in recent years. However, most of this work focuses on widely-used general purpose programming languages. The utility of LLMs for software within the industrial process automation domain, with highly-specialized languages that are typically only used in proprietary contexts, is still underexplored. Within this paper, we study enterprises can achieve on their own without investing large amounts of effort into the training of models specific to the domain-specific languages that are used. We show that few-shot prompting approaches are sufficient to solve simple problems in a language that is otherwise not well-supported by an LLM and that is possible on-premise, thereby ensuring the protection of sensitive company data.

Many Knowledege Graphs (KGs) are frequently updated, forcing their Knowledge Graph Embeddings (KGEs) to adapt to these changes. To address this problem, continual learning techniques for KGEs incorporate embeddings for new entities while updating the old ones. One necessary step in these methods is the initialization of the embeddings, as an input to the KGE learning process, which can have an important impact in the accuracy of the final embeddings, as well as in the time required to train them. This is especially relevant for relatively small and frequent updates. We propose a novel informed embedding initialization strategy, which can be seamlessly integrated into existing continual learning methods for KGE, that enhances the acquisition of new knowledge while reducing catastrophic forgetting. Specifically, the KG schema and the previously learned embeddings are utilized to obtain initial representations for the new entities, based on the classes the entities belong to. Our extensive experimental analysis shows that the proposed initialization strategy improves the predictive performance of the resulting KGEs, while also enhancing knowledge retention. Furthermore, our approach accelerates knowledge acquisition, reducing the number of epochs, and therefore time, required to incrementally learn new embeddings. Finally, its benefits across various types of KGE learning models are demonstrated.

Reinforcement fine-tuning (RFT), a two-stage framework consisting of supervised fine-tuning (SFT) and reinforcement learning (RL) has shown promising results on improving reasoning ability of large language models (LLMs). Yet extending RFT to large video language models (LVLMs) remains challenging. We propose VideoP2R, a novel process-aware video RFT framework that enhances video reasoning by modeling perception and reasoning as distinct processes. In the SFT stage, we develop a three-step pipeline to generate VideoP2R-CoT-162K, a high-quality, process-aware chain-of-thought (CoT) dataset for perception and reasoning. In the RL stage, we introduce a novel process-aware group relative policy optimization (PA-GRPO) algorithm that supplies separate rewards for perception and reasoning. Extensive experiments show that VideoP2R achieves state-of-the-art (SotA) performance on six out of seven video reasoning and understanding benchmarks. Ablation studies further confirm the effectiveness of our process-aware modeling and PA-GRPO and demonstrate that model's perception output is information-sufficient for downstream reasoning.