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This research develops predictive surrogate models that combine data-driven machine learning (e.g., LSTM) with hybrid physics-based enhancements such as physics-informed constraints. Using a process plant case study with real, simulated, and synthetic data from a digital twin and soft sensors, the work constructs training and testing datasets from sparsely available measurements and compares forecasting accuracy between data-driven and hybrid approaches.","This document is downloaded from the VTT Research Information Portal  \n[https://cris.vtt.fi](https://cris.vtt.fi)  \nVTT Technical Research Centre of Finland  \nForecasting Process Output using Machine Learning Surrogates and Digital Twin  \nSeppi, Mikko; Linnosmaa, Joonas; Zeb, Akhtar  \nPublished in:  \nNuclear Plant Instrumentation and Control & Human-Machine Interface Technology (NPIC&HMIT 2025)  \nDOI:  \n10.13182/xyz-46675  \nPublished: 01/01/2025  \nDocument Version  \nEarly version, also known as pre-print  \nLink to publication  \nPlease cite the original version:  \nSeppi, M. , Linnosmaa, J. , & Zeb, A. (2025) . Forecasting Process Output using Machine Learning Surrogatesand Digital Twin. In Nuclear Plant Instrumentation and Control & Human-Machine Interface Technology (NPIC&HMIT 2025) (pp. 434-443) . American Nuclear Society (ANS) . [https://doi.org/10.13182/xyz-46675](https://doi.org/10.13182/xyz-46675)  \nVTT  \n[https://www.vttresearch.com](https://www.vttresearch.com)  \nVTT Technical Research Centre of Finland Ltd  \n[P.O. box 1000](P.O. box 1000)[ ](P.O. box 1000)[FI-02044 VTT](FI-02044 VTT)[ ](FI-02044 VTT)Finland  \nBy using VTT Research Information Portal you are bound by the following Terms & Conditions.  \nI have read and I understand the following statement:  \nThis document is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of this document is not permitted, except duplication for research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered for sale.  \nDownload date: 08. Mar. 2026  \nForecasting Process Output using Machine Learning Surrogates and Digital Twin  \nMikko Seppi 1∗, Joonas Linnosmaa 1 , Akhtar Zeb 1  \n1VTT Technical Research Centre of Finland Ltd, Espoo, Finland  \nABSTRACT  \nTime series prediction and simulation are crucial across various real-life applications. Our research specifically tackles the challenges of multivariate, multi-step forecasting which involves predicting future behavior over multiple time steps, a task where model uncertainty accumulates, complicating accuracy and interpretability. Unlike univariate models, multivariate analysis must handle complex interdependencies among multiple variables, which increases both the complexity and the computational demand.  \nTo manage these complexities, our work explores the development of predictive surrogates that integrate both data-driven machine learning techniques (such as LSTM) and hybrid methods incorporating physics-based enhancements (like physics-based constraints) . Utilizing a process plant as our case study, we have constructed these surrogates using a blend of real, simulated, and synthetic data from the plant, a digital twin, and soft sensors. Our methodologies extend to crafting appropriate training and testing datasets from sparsely available real data.  \nThe results from our research project demonstrate the differences in forecasting accuracy between data-driven and hybrid models. We discuss the comparative benefits of each model and share insights gained from the integration of machine learning and physical models for multi-step prediction. Looking forward, we aim to refine these predictive surrogate models further to enhance their predictive performance and operational applicability in process control and optimization.  \nKeywords: Deep learning, Time series forecasting, Digital twin, Surrogate model, Physics-informed machine learning  \n1. INTRODUCTION  \nThe integration of digital twin technology in industrial processes has received significant attention due its potential to enchance operational efficiency and decision making. In the nuclear industry, the deployment of digital twins can significantly improve the safety, reliability, and performance of complex systems. This paper presents the findings of two studies: one on purely data-driven machine learning (ML) surrogate models [1","cbCaitB1Yqpe2C4c","https://ap.wps.com/l/cbCaitB1Yqpe2C4c","pdf",2956844,1,11,"English","en",105,"# Abstract\n# Introduction\n## Digital twin in industrial and nuclear processes\n## Research objective and surrogate model types\n## Multi-step multivariate forecasting challenges\n# Background and related work\n# Digital twin and process description\n# Dataset preparation","[{\"question\":\"What forecasting problem does the research focus on?\",\"answer\":\"The study targets multivariate, multi-step time-series forecasting, predicting future system behavior across multiple time steps while addressing accumulated uncertainty.\"},{\"question\":\"How do the surrogate models differ between data-driven and hybrid approaches?\",\"answer\":\"One model is trained purely with data-driven machine learning (LSTM), while the hybrid model incorporates physics-based constraints during training to improve reliability and prediction quality.\"},{\"question\":\"What data sources are used to build and train the surrogates?\",\"answer\":\"The approach blends real, simulated, and synthetic data, leveraging a digital twin and soft sensors, and creates training/testing datasets from sparsely available real measurements.\"}]","Forecasting Process Output using Machine Learning Surrogates and Digital Twin | 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