Continuous-Time Piecewise-Linear Recurrent Neural Networks

In dynamical systems reconstruction (DSR) we aim to recover the dynamical system (DS) underlying observed time series. Specifically, we aim to learn a generative surrogate model which approximates the underlying, data-generating DS, and recreates its long-term properties (`climate statistics'). In scientific and medical areas, in particular, these models need to be mechanistically tractable -- through their mathematical analysis we would like to obtain insight into the recovered system's workings. Piecewise-linear (PL), ReLU-based RNNs (PLRNNs) have a strong track-record in this regard, representing SOTA DSR models while allowing mathematical insight by virtue of their PL design. However, all current PLRNN variants are discrete-time maps. This is in disaccord with the assumed continuous-time nature of most physical and biological processes, and makes it hard to accommodate data arriving at irregular temporal intervals. Neural ODEs are one solution, but they do not reach the DSR performance of PLRNNs and often lack their tractability. Here we develop theory for continuous-time PLRNNs (cPLRNNs): We present a novel algorithm for training and simulating such models, bypassing numerical integration by efficiently exploiting their PL structure. We further demonstrate how important topological objects like equilibria or limit cycles can be determined semi-analytically in trained models. We compare cPLRNNs to both their discrete-time cousins as well as Neural ODEs on DSR benchmarks, including systems with discontinuities which come with hard thresholds.

It's TIME: Towards the Next Generation of Time Series Forecasting Benchmarks

Time series foundation models (TSFMs) are revolutionizing the forecasting landscape from specific dataset modeling to generalizable task evaluation. However, we contend that existing benchmarks exhibit common limitations in four dimensions: constrained data composition dominated by reused legacy sources, compromised data integrity lacking rigorous quality assurance, misaligned task formulations detached from real-world contexts, and rigid analysis perspectives that obscure generalizable insights. To bridge these gaps, we introduce TIME, a next-generation task-centric benchmark comprising 50 fresh datasets and 98 forecasting tasks, tailored for strict zero-shot TSFM evaluation free from data leakage. Integrating large language models and human expertise, we establish a rigorous human-in-the-loop benchmark construction pipeline to ensure high data integrity and redefine task formulation by aligning forecasting configurations with real-world operational requirements and variate predictability. Furthermore, we propose a novel pattern-level evaluation perspective that moves beyond traditional dataset-level evaluations based on static meta labels. By leveraging structural time series features to characterize intrinsic temporal properties, this approach offers generalizable insights into model capabilities across diverse patterns. We evaluate 12 representative TSFMs and establish a multi-granular leaderboard to facilitate in-depth analysis and visualized inspection. The leaderboard is available at https://huggingface.co/spaces/Real-TSF/TIME-leaderboard.

Power Interpretable Causal ODE Networks: A Unified Model for Explainable Anomaly Detection and Root Cause Analysis in Power Systems

Anomaly detection and root cause analysis (RCA) are critical for ensuring the safety and resilience of cyber-physical systems such as power grids. However, existing machine learning models for time series anomaly detection often operate as black boxes, offering only binary outputs without any explanation, such as identifying anomaly type and origin. To address this challenge, we propose Power Interpretable Causality Ordinary Differential Equation (PICODE) Networks, a unified, causality-informed architecture that jointly performs anomaly detection along with the explanation why it is detected as an anomaly, including root cause localization, anomaly type classification, and anomaly shape characterization. Experimental results in power systems demonstrate that PICODE achieves competitive detection performance while offering improved interpretability and reduced reliance on labeled data or external causal graphs. We provide theoretical results demonstrating the alignment between the shape of anomaly functions and the changes in the weights of the extracted causal graphs.

Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems

Root cause analysis (RCA) in networked industrial systems, such as supply chains and power networks, is notoriously difficult due to unknown and dynamically evolving interdependencies among geographically distributed clients. These clients represent heterogeneous physical processes and industrial assets equipped with sensors that generate large volumes of nonlinear, high-dimensional, and heterogeneous IoT data. Classical RCA methods require partial or full knowledge of the system's dependency graph, which is rarely available in these complex networks. While federated learning (FL) offers a natural framework for decentralized settings, most existing FL methods assume homogeneous feature spaces and retrainable client models. These assumptions are not compatible with our problem setting. Different clients have different data features and often run fixed, proprietary models that cannot be modified. This paper presents a federated cross-client interdependency learning methodology for feature-partitioned, nonlinear time-series data, without requiring access to raw sensor streams or modifying proprietary client models. Each proprietary local client model is augmented with a Machine Learning (ML) model that encodes cross-client interdependencies. These ML models are coordinated via a global server that enforces representation consistency while preserving privacy through calibrated differential privacy noise. RCA is performed using model residuals and anomaly flags. We establish theoretical convergence guarantees and validate our approach on extensive simulations and a real-world industrial cybersecurity dataset.

AWGformer: Adaptive Wavelet-Guided Transformer for Multi-Resolution Time Series Forecasting

Time series forecasting requires capturing patterns across multiple temporal scales while maintaining computational efficiency. This paper introduces AWGformer, a novel architecture that integrates adaptive wavelet decomposition with cross-scale attention mechanisms for enhanced multi-variate time series prediction. Our approach comprises: (1) an Adaptive Wavelet Decomposition Module (AWDM) that dynamically selects optimal wavelet bases and decomposition levels based on signal characteristics; (2) a Cross-Scale Feature Fusion (CSFF) mechanism that captures interactions between different frequency bands through learnable coupling matrices; (3) a Frequency-Aware Multi-Head Attention (FAMA) module that weights attention heads according to their frequency selectivity; (4) a Hierarchical Prediction Network (HPN) that generates forecasts at multiple resolutions before reconstruction. Extensive experiments on benchmark datasets demonstrate that AWGformer achieves significant average improvements over state-of-the-art methods, with particular effectiveness on multi-scale and non-stationary time series. Theoretical analysis provides convergence guarantees and establishes the connection between our wavelet-guided attention and classical signal processing principles.

TS-Debate: Multimodal Collaborative Debate for Zero-Shot Time Series Reasoning

Recent progress at the intersection of large language models (LLMs) and time series (TS) analysis has revealed both promise and fragility. While LLMs can reason over temporal structure given carefully engineered context, they often struggle with numeric fidelity, modality interference, and principled cross-modal integration. We present TS-Debate, a modality-specialized, collaborative multi-agent debate framework for zero-shot time series reasoning. TS-Debate assigns dedicated expert agents to textual context, visual patterns, and numerical signals, preceded by explicit domain knowledge elicitation, and coordinates their interaction via a structured debate protocol. Reviewer agents evaluate agent claims using a verification-conflict-calibration mechanism, supported by lightweight code execution and numerical lookup for programmatic verification. This architecture preserves modality fidelity, exposes conflicting evidence, and mitigates numeric hallucinations without task-specific fine-tuning. Across 20 tasks spanning three public benchmarks, TS-Debate achieves consistent and significant performance improvements over strong baselines, including standard multimodal debate in which all agents observe all inputs.

From Signals to Causes: A Causal Signal Processing Framework for Robust and Interpretable Clinical Risk Prediction

Learning-based signal processing systems increasingly support high-stakes medical decisions using heterogeneous biomedical signals, including medical images, physiological time series, and clinical records. Despite strong predictive performance, many models rely on statistical correlations that are unstable across acquisition settings, patient populations, and institutional practices, limiting robustness, interpretability, and clinical trust. We advocate a causal signal processing perspective in which biomedical signals are treated as effects of latent generative mechanisms rather than as isolated predictive inputs. Using clinical risk prediction as a motivating example, we show how disease-related factors generate observable biomarkers, while acquisition processes act as confounders influencing signal appearance. In clinical disease risk prediction from chest CT scans and patient risk factors, correlational models may fail under scanner changes, whereas causal abstractions remain invariant. Building on this view, we propose a unifying conceptual framework integrating causal modeling with learning-based signal processing and neuro-symbolic reasoning. Statistical models extract multimodal representations that are mapped to interpretable causal abstractions and combined with symbolic knowledge encoding clinical risk factors and guidelines. This structure enables clinically grounded explanations, counterfactual reasoning about hypothetical interventions, and improved robustness to distribution shifts arising from changes in acquisition conditions or screening policies. Rather than introducing a specific algorithm, this article presents schematic causal structures and a comparative analysis of correlation-based, causal, and neuro-symbolic approaches to guide the design of robust and interpretable medical decision-support systems.

AgriWorld:A World Tools Protocol Framework for Verifiable Agricultural Reasoning with Code-Executing LLM Agents

Foundation models for agriculture are increasingly trained on massive spatiotemporal data (e.g., multi-spectral remote sensing, soil grids, and field-level management logs) and achieve strong performance on forecasting and monitoring. However, these models lack language-based reasoning and interactive capabilities, limiting their usefulness in real-world agronomic workflows. Meanwhile, large language models (LLMs) excel at interpreting and generating text, but cannot directly reason over high-dimensional, heterogeneous agricultural datasets. We bridge this gap with an agentic framework for agricultural science. It provides a Python execution environment, AgriWorld, exposing unified tools for geospatial queries over field parcels, remote-sensing time-series analytics, crop growth simulation, and task-specific predictors (e.g., yield, stress, and disease risk). On top of this environment, we design a multi-turn LLM agent, Agro-Reflective, that iteratively writes code, observes execution results, and refines its analysis via an execute-observe-refine loop. We introduce AgroBench, with scalable data generation for diverse agricultural QA spanning lookups, forecasting, anomaly detection, and counterfactual "what-if" analysis. Experiments outperform text-only and direct tool-use baselines, validating execution-driven reflection for reliable agricultural reasoning.

Position: Why a Dynamical Systems Perspective is Needed to Advance Time Series Modeling

Time series (TS) modeling has come a long way from early statistical, mainly linear, approaches to the current trend in TS foundation models. With a lot of hype and industrial demand in this field, it is not always clear how much progress there really is. To advance TS forecasting and analysis to the next level, here we argue that the field needs a dynamical systems (DS) perspective. TS of observations from natural or engineered systems almost always originate from some underlying DS, and arguably access to its governing equations would yield theoretically optimal forecasts. This is the promise of DS reconstruction (DSR), a class of ML/AI approaches that aim to infer surrogate models of the underlying DS from data. But models based on DS principles offer other profound advantages: Beyond short-term forecasts, they enable to predict the long-term statistics of an observed system, which in many practical scenarios may be the more relevant quantities. DS theory furthermore provides domain-independent theoretical insight into mechanisms underlying TS generation, and thereby will inform us, e.g., about upper bounds on performance of any TS model, generalization into unseen regimes as in tipping points, or potential control strategies. After reviewing some of the central concepts, methods, measures, and models in DS theory and DSR, we will discuss how insights from this field can advance TS modeling in crucial ways, enabling better forecasting with much lower computational and memory footprints. We conclude with a number of specific suggestions for translating insights from DSR into TS modeling.

Real time fault detection in 3D printers using Convolutional Neural Networks and acoustic signals

The reliability and quality of 3D printing processes are critically dependent on the timely detection of mechanical faults. Traditional monitoring methods often rely on visual inspection and hardware sensors, which can be both costly and limited in scope. This paper explores a scalable and contactless method for the use of real-time audio signal analysis for detecting mechanical faults in 3D printers. By capturing and classifying acoustic emissions during the printing process, we aim to identify common faults such as nozzle clogging, filament breakage, pully skipping and various other mechanical faults. Utilizing Convolutional neural networks, we implement algorithms capable of real-time audio classification to detect these faults promptly. Our methodology involves conducting a series of controlled experiments to gather audio data, followed by the application of advanced machine learning models for fault detection. Additionally, we review existing literature on audio-based fault detection in manufacturing and 3D printing to contextualize our research within the broader field. Preliminary results demonstrate that audio signals, when analyzed with machine learning techniques, provide a reliable and cost-effective means of enhancing real-time fault detection.