# Hybrid Meta-Learning Framework for Anomaly Forecasting in Nonlinear Dynamical Systems via Physics-Inspired Simulation and Deep Ensembles

arXiv: https://arxiv.org/abs/2506.13828 · HTML: https://mlsanity.com/paper/2506.13828/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 4 of 4)

- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection](https://mlsanity.com/paper/1607.00148/) (2016)
- [Anomaly Detection Based on Isolation Mechanisms: A Survey](https://mlsanity.com/paper/2403.10802/) (2024)
- [DA-LSTM: A Dynamic Drift-Adaptive Learning Framework for Interval Load Forecasting with LSTM Networks](https://mlsanity.com/paper/2305.08767/) (2023)

## Abstract (arXiv)

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures nonlinear growth-relaxation dynamics with random perturbations, representative of many complex physical, industrial, and cyber-physical systems. We use CNN-LSTM architectures for spatio-temporal feature extraction, Variational Autoencoders (VAE) for unsupervised anomaly scoring, and Isolation Forests for residual-based outlier detection in addition to a Dual-Stage Attention Recurrent Neural Network (DA-RNN) for one-step forecasting on top of the generated simulation data. To create composite anomaly forecasts, these models are combined using a meta-learner that combines forecasting outputs, reconstruction errors, and residual scores. The hybrid ensemble performs better than standalone models in anomaly localization, generalization, and robustness to nonlinear deviations, according to simulation-based experiments. The framework provides a broad, data-driven approach to early defect identification and predictive monitoring in nonlinear systems, which may be applied to a variety of scenarios where complete physical models might not be accessible.