{
  "annotation_id": "aff5f6e7-5e9c-42ef-b1b1-7b7306a58370",
  "date_created": "2026-02-17T05:53:11.626000Z",
  "date_modified": "2026-02-17T05:53:11.626000Z",
  "file_hash": "2f12724e284f9c3259f640230a816f19462167e7c8871ebb57b5fbf0f3d6c87f",
  "private": false,
  "record": {
    "abstract": "This paper develops an approach for multi-step forecasting of dynamical systems by integrating probabilistic input forecasting with physics-informed output prediction. Accurate multi-step forecasting of time series systems is important for the automatic control and optimization of physical processes, enabling more precise decision-making. While mechanistic-based and data-driven machine learning (ML) approaches have been employed for time series forecasting, they face significant limitations. Incomplete knowledge of process mathematical models limits mechanistic-based direct employment, while purely data-driven ML models struggle with dynamic environments, leading to poor generalization. To address these limitations, this paper proposes a dual-level strategy for physics-informed forecasting of dynamical systems. On the first level, input variables are forecast using a hybrid method that integrates a long short-term memory (LSTM) network into probabilistic state transition models (STMs). On the second level, these stochastically predicted inputs are sequentially fed into a physics-informed neural network (PINN) to generate multi-step output predictions. The experimental results of the paper demonstrate that the hybrid input forecasting models achieve a higher log-likelihood and lower mean squared errors (MSE) compared to conventional STMs. Furthermore, the PINNs driven by the input forecasting models outperform their purely data-driven counterparts in terms of MSE and log-likelihood, exhibiting stronger generalization and forecasting performance across multiple test cases.",
    "arxiv_id": "2601.07640",
    "authors": [
      "Mahdi Nasiri",
      "Johanna Kortelainen",
      "Simo S\u00e4rkk\u00e4"
    ],
    "categories": [
      "stat.ML",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "title": "Dual-Level Models for Physics-Informed Multi-Step Time Series Forecasting",
    "url": "https://arxiv.org/abs/2601.07640",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e57ea8f3-6418-46b6-b5e5-7299640e70ef",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}