Ecological systems exhibit complex multi-scale dynamics that challenge traditional modeling. New methods must capture temporal oscillations and emergent spatiotemporal patterns while adhering to conservation principles. We present the Unified Spatiotemporal Physics-Informed Learning (USPIL) framework, a deep learning architecture integrating physics-informed neural networks (PINNs) and conservation laws to model predator-prey dynamics across dimensional scales. The framework provides a unified solution for both ordinary (ODE) and partial (PDE) differential equation systems, describing temporal cycles and reaction-diffusion patterns within a single neural network architecture. Our methodology uses automatic differentiation to enforce physics constraints and adaptive loss weighting to balance data fidelity with physical consistency. Applied to the Lotka-Volterra system, USPIL achieves 98.9% correlation for 1D temporal dynamics (loss: 0.0219, MAE: 0.0184) and captures complex spiral waves in 2D systems (loss: 4.7656, pattern correlation: 0.94). Validation confirms conservation law adherence within 0.5% and shows a 10-50x computational speedup for inference compared to numerical solvers. USPIL also enables mechanistic understanding through interpretable physics constraints, facilitating parameter discovery and sensitivity analysis not possible with purely data-driven methods. Its ability to transition between dimensional formulations opens new avenues for multi-scale ecological modeling. These capabilities make USPIL a transformative tool for ecological forecasting, conservation planning, and understanding ecosystem resilience, establishing physics-informed deep learning as a powerful and scientifically rigorous paradigm.

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One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.

A B S T R A C T We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby reducing the effective dimensionality of training while preserving solution accuracy. The low-rank tangent subspace is defined layer-wise by the singular value decomposition (SVD) of the current network weights, and the resulting update is obtained by solving a well-posed, tractable linear system within this subspace. We evaluate LR-EDNN on representative PDE problems and compare it against corresponding baselines. Across cases, LR-EDNN achieves comparable accuracy with substantially fewer trainable parameters and reduced computational cost. These results indicate that low-rank constraints on parameter velocities, rather than full-space updates, provide a practical path toward scalable, efficient, and reproducible scientific machine learning for PDEs. Introduction The application of deep learning to solving partial differential equations (PDEs) has emerged as an active and promising research area, providing a powerful alternative to traditional numerical methods. Unlike classical approaches such as finite difference, finite element, or spectral methods, which rely on discretization and iterative solvers, deep learning methods leverage neural networks to approximate solutions directly, often bypassing the need for meshes and offering flexibility in handling irregular domains and high-dimensional problems [1, 2]. Early efforts in this domain focused primarily on two paradigms.

Manual HVAC fault diagnosis in commercial buildings takes 8-12 hours per incident and achieves only 60 percent diagnostic accuracy, reflecting analytics that stop at correlation instead of causation. To close this gap, we present GRID (Graph-based Reasoning for Intervention and Discovery), a three-stage causal discovery pipeline that combines constraint-based search, neural structural equation modeling, and language model priors to recover directed acyclic graphs from building sensor data. Across six benchmarks: synthetic rooms, EnergyPlus simulation, the ASHRAE Great Energy Predictor III dataset, and a live office testbed, GRID achieves F1 scores ranging from 0.65 to 1.00, with exact recovery (F1 = 1.00) in three controlled environments (Base, Hidden, Physical) and strong performance on real-world data (F1 = 0.89 on ASHRAE, 0.86 in noisy conditions). The method outperforms ten baseline approaches across all evaluation scenarios. Intervention scheduling achieves low operational impact in most scenarios (cost <= 0.026) while reducing risk metrics compared to baseline approaches. The framework integrates constraint-based methods, neural architectures, and domain-specific language model prompts to address the observational-causal gap in building analytics.

Developing trustworthy intelligent vision systems for high-stakes domains, \emph{e.g.}, remote sensing and medical diagnosis, demands broad robustness without costly retraining. We propose \textbf{Visual Reasoning Agent (VRA)}, a training-free, agentic reasoning framework that wraps off-the-shelf vision-language models \emph{and} pure vision systems in a \emph{Think--Critique--Act} loop. While VRA incurs significant additional test-time computation, it achieves up to 40\% absolute accuracy gains on challenging visual reasoning benchmarks. Future work will optimize query routing and early stopping to reduce inference overhead while preserving reliability in vision tasks.

This study deploys methods in explainable artificial intelligence (XAI), e.g. decision trees and Pearson's correlation coefficient (PCC), to investigate electricity usage in multiple locales. It addresses the vital issue of energy burden, i.e. total amount spent on energy divided by median household income. Socio-demographic data is analyzed with energy features, especially using decision trees and PCC, providing explainable predictors on factors affecting energy burden. Based on the results of the analysis, a pilot energy equity web portal is designed along with a novel energy burden calculator. Leveraging XAI, this portal (with its calculator) serves as a prototype information system that can offer tailored actionable advice to multiple energy stakeholders. The ultimate goal of this study is to promote greater energy equity through the adaptation of XAI methods for energy-related analysis with suitable recommendations.

We present EPIC, an AI-driven platform designed to augment operational data analytics. EPIC employs a hierarchical multi-agent architecture where a top-level large language model provides query processing, reasoning and synthesis capabilities. These capabilities orchestrate three specialized low-level agents for information retrieval, descriptive analytics, and predictive analytics. This architecture enables EPIC to perform HPC operational analytics on multi-modal data, including text, images, and tabular formats, dynamically and iteratively. EPIC addresses the limitations of existing HPC operational analytics approaches, which rely on static methods that struggle to adapt to evolving analytics tasks and stakeholder demands. Through extensive evaluations on the Frontier HPC system, we demonstrate that EPIC effectively handles complex queries. Using descriptive analytics as a use case, fine-tuned smaller models outperform large state-of-the-art foundation models, achieving up to 26% higher accuracy. Additionally, we achieved 19x savings in LLM operational costs compared to proprietary solutions by employing a hybrid approach that combines large foundational models with fine-tuned local open-weight models.