Application of Digital Twins to Large-Scale Complex Systems

In this talk we do introduce surrogate approaches by combining model reduction with physics informed machine learning for applications in design, optimisation, as well as digital twins. Reduced-order models (ROMs) are essential for enabling efficient and accurate simulations of complex physical phenomena, particularly in Computational Fluid Dynamics (CFD) and fluid-structure interaction. We do focus on recent advancements in enhancing ROM techniques to address the challenges of real-time, multi-query, and multi-physics applications. We will explore strategies to improve the accuracy and efficiency of ROMs by integrating advanced methodologies such as neural operators and optimisation-based frameworks. These approaches leverage both physics-based insights and data-driven models to create enhanced ROMs that outperform traditional methods in terms of generalisation and computational cost. Applications to CFD, including turbulent and compressible flows, demonstrate the impact of these improvements in achieving precise and reliable solutions. These strategies extend the applicability of ROMs to complex multi-physics and multi-scale problems, offering new possibilities for simulation-driven discovery and design. This talk underlines their transformative potential in advancing computational science and engineering by highlighting cutting-edge techniques for enhancing ROMs.

At Michelin, the digital twin is at the heart of the group's R&D strategy. Using modern model reduction and machine learning techniques, virtual tires are now used for in-house design, in driving simulators, and to define tire-oriented services for our customers. Beyond tires, simulation and data science play a key role across the product lifecycle. During the talk, we will introduce the global context of simulation and data science usage at Michelin R&D. Then, we will focus on three example applications combining physics-based models, reduced-order modeling, physics-informed machine learning, and data assimilation techniques: (1) predicting rubber mix behavior during the manufacturing phase, (2) assessing tire hydroplaning performance during the design phase, and (3) estimating real-time tire grip during the usage phase. These examples will illustrate how hybrid approaches leveraging physics and data are paving the way toward robust, efficient, and versatile digital twins.

Industrial manufacturing often involves large-scale, multistage systems in which the output of one stage becomes the input of the next. Building real-time digital twins for such hierarchical and strongly coupled processes remains challenging despite major recent advances in sensing, data infrastructure, and computational power. Large-scale industrial systems typically exhibit complex topologies, nonlinear interations across units, and time-varying operational constraints, all of which complicate both their virtual representation and their optimization. This work presents a unified framework for constructing digital twins of multilevel industrial systems that integrates topological optimization of system architecture with parametric optimization of process controls. The proposed methodology uses first-principles modeling to ensure physical consistency while maintaining real-time computational performance. A hierarchical decomposi$on strategy is introduced to manage scale, enabling local digital twins for individual units to be seamlessly embedded within a global system-level twin. The resulting digital twin allows evaluating alternative configurations or parameter settngs to improve reliability and reduce raw material consumption. A case studies is represented for a large-scale manufacturing process demonstrates the approach. Moreover, topological optimization through novel projection-based neural architecture is discussed.

Introduction Software development is undergoing a paradigm shift from explicit programming (“Software 1.0”) toward software learned from data (“Software 2.0”) [1]. This evolution has now progressed to the era of “Software 3.0,” in which natural language serves as the programming interface and large pretrained models handle the rest [2]. In this new paradigm, large language models (LLMs) function as versatile general purpose reasoning engines, allowing developers to articulate goals in plain English and have the model generate the corresponding solutions [3]. The impact of this shift extends far beyond computer science: foundation models are already driving advances in biomedical research and healthcare [4], education [5, 6], and high-stakes fields such as finance, consulting, and law [7]. Drawing an analogy from engineering software in computer-aided engineering (CAE), Software 1.0 corresponds to classical finite element analysis (FEA) solvers, where engineers hand-coded numerical formulations (e.g., Ansys, Abaqus, etc.) [8]. Software 2.0 introduced data-driven surrogate modelling, where machine learning was used to approximate high-fidelity simulations [9]. Software 3.0 aims to combine the strengths of both worlds: embedding engineering domain knowledge into LLMs that can understand context, retrieve relevant information from a stack of domain expertise, and generate solutions or insights on demand. While recent uses of LLMs in CAE have automated tasks such as CAD model generation or FEM simulations [10], these applications largely replicate tasks that human experts can already perform. In this talk, we introduce how the Software 3.0 framework can convey transformative advances CAE, highlighting its applications to digital twins, additive manufacturing, and electronic design automation [11]. Software 3.0 in CAE 2.1. Agentic AI via model context protocol (MCP) for digital twins Agentic AI refers to AI systems that move beyond passively assisting engineers and instead act as autonomous collaborators capable of planning, executing, and adapting CAE workflows. Enabled by the Model Context Protocol (MCP), which standardizes communication between LLMs and software tools, such systems can dynamically invoke functions for geometry import, meshing, solver execution, data processing, and surrogate modelling. This workflow supports the creation and operation of digital twins by automating decision-making steps, such as selecting sampling strategies or training models, that are typically problem dependent and reached through trial and error. As MCP tools accumulate into a scalable knowledge base, annotated by engineers and interpretable by LLMs, agentic AI can leverage this collective expertise to accelerate exploration of parameter spaces, enhance computational efficiency, and deliver adaptive digital twin simulations. 2.2. Automated solver development for intrusive model order reduction (MOR) for space-parameter-time forward and inversed engineering problems A transformative opportunity for CAE lies in automated solver development for intrusive model order reduction (MOR), which reduces the computational burden of large-scale simulations that prevail in additive manufacturing and electronic design automation while preserving accuracy. Unlike non-intrusive data-driven surrogates, intrusive MOR directly modifies governing equations to create efficient, data-free reduced-order models, but its adoption has been limited by the difficulty of redeveloping complex solvers. Recent advances in LLMs offer a pathway to overcome this barrier by automating algebraic derivations, code restructuring, and solver implementation, enabling engineers to generate high-fidelity reduced-order models with natural language prompts. We demonstrate this capability through Tensor-decomposition-based A Priori Surrogates (TAPS) [12], showing how LLMs can reduce development effort while meeting key performance metrics of accuracy, speed, and efficiency. This workflow holds promise for accelerating digital twin applications in additive manufacturing and electronic design automation, where scalable and adaptive reduced-order models are critical for design and optimization. Wing Kam Liu*, Chanwook Park+, Jiachen Guo+, Gino Domel*, Hantao Zhang+ *Northwestern University, HIDENN-AI, LLC +Northwestern University References Karpathy, A., Software 2.0. 2017. Karpathy, A., Software 3.0. 2025. Raiaan, M.A.K., et al., A review on large language models: Architectures, applications, taxonomies, open issues and challenges. IEEE access, 2024. 12: p. 26839-26874. Nazi, Z.A. and W. Peng. Large language models in healthcare and medical domain: A review. in Informatics. 2024. MDPI. Kasneci, E., et al., ChatGPT for good? On opportunities and challenges of large language models for education. Learning and individual differences, 2023. 103: p. 102274. Jeon, J. and S. Lee, Large language models in education: A focus on the complementary relationship between human teachers and ChatGPT. Education and Information Technologies, 2023. 28(12): p. 15873-15892. Chen, Z.Z., et al., A survey on large language models for critical societal domains: Finance, healthcare, and law. arXiv preprint arXiv:2405.01769, 2024. Liu, W.K., S. Li, and H.S. Park, Eighty years of the finite element method: Birth, evolution, and future. Archives of Computational Methods in Engineering, 2022. 29(6): p. 4431-4453. Guo, J., et al., Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems. arXiv preprint arXiv:2503.02041, 2025. Zhang, L., et al., Large language models for computer-aided design: A survey. arXiv preprint arXiv:2505.08137, 2025. Guo, J., et al., AI-Empowered CAE via Software 3.0. In prep, 2025. Guo, J., et al., Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations. Computer Methods in Applied Mechanics and Engineering, 2025. 444: p. 118101.

In this talk, we explore (i) how we can use pre-existing knowledge (e.g., physics) to improve AI systems, and (ii) how we can possible extract some knowledge from AI systems. On the first topic, we present a novel physics-enhanced deep learning hybrid method, namely CondensNet, for resolving cloud physics in general circulation models. On the second topic, we present some results on the use of explainable AI for Earth System applications in the context of extreme events. We conclude with an overall perspective bridging the two topics and grounded in the digital twin paradigm.

We introduce a nonlinear interpolation framework for parametric fields that relies on a variational mapping approach to track and align coherent structures across parameter values. Starting from high-fidelity simulations, we employ scalar sensors to extract point clouds representing key solution features—such as shocks, shear layers, or other coherent structures—and use registration techniques to construct bijective domain mappings that allow accurate nonlinear interpolations. Within the parametric model order reduction setting, these variational procedures exploit solution snapshots to identify coordinate transformations that improve the approximation of the solution set. Optimization-based methods minimize a target function measuring the alignment of coherent structures across the parameter domain, over a family of bijections defined on a bounded domain. We consider diffeomorphisms generated as vector flows of velocity fields with vanishing normal component on parts of the domain boundary; we rely on a sensor to extract point clouds from the collected solution snapshots and develop an expectation–maximization strategy to simultaneously solve the point cloud matching problem and determine the mapping. We then combine the resulting registration with convex displacement interpolation [Iollo, Taddei, J. Comput. Phys., 2022] to obtain accurate interpolations of fluid-dynamic fields in the presence of shocks. Numerical results for a two-dimensional inviscid transonic flow past a NACA airfoil and a three-dimensional viscous transonic flow past an ONERA M6 wing illustrate the key components of the methodology and demonstrate the effectiveness of nonlinear interpolation for shock-dominated regimes. Work with Jean-Baptiste Chapelier, Jon Labatut and Tommaso Taddei

Most approaches for solving partial differential equations rely on generating a mesh that captures the geometry of the model. At present, unstructured mesh technology is the dominant choice, making it possible to create three-dimensional meshes with hundreds of millions of elements within minutes. Yet, when performing design optimisation, multiple simulations are required for varying operating conditions and geometric configurations. Producing a high-quality mesh for each case is extremely time-consuming, as it demands substantial human input and specialised expertise. In this presentation, I will discuss our recent research on applying artificial intelligence to predict near-optimal meshes for simulation purposes. The central idea is to exploit the wealth of industrial data already available to improve the selection of an appropriate spacing function, including anisotropic distributions. The method seeks to transfer knowledge from past simulations to guide the meshing process more effectively. I will evaluate this approach in terms of prediction accuracy, computational efficiency, and sustainability, considering the carbon footprint and energy demands associated with parametric CFD studies across a range of flow conditions and angles of attack.

The consideration of fundamental physical laws when performing machine learning predictions within the fields of materials mechanics and processing of large-scale complex systems, can reduce errors and enhance generalization. While physics-based models contain assumptions and simplifications; thus, produce errors, data-driven models can demand relatively large data sets to represent fundamental relationships. These respective disadvantages can be compensated for via a synergistic combination of both modelling methods. A particular hybrid modeling approach is given by a physics-based model (either analytical or numerical) that is data-mined and corrected via a data-driven discrepancy model to reach the desired reference solution, in this work stemming from either experimental measurements or high-fidelity simulations. The prediction targets span from process behavior and process temperature to resulting material properties of complex processes. A number of different application examples are presented for a variety of materials processing techniques, such as Laser-Shock-Peening, a technique used for the modification of residual stresses in metallic materials; Friction Surfacing, a solid-state processing technique of metallic materials used for additive manufacturing; as well as Hot Rolling, whereby metal strips with specific geometries and mechanical properties are produced. Additionally, physics-based feature engineering via dimensionless formulations of inputs and outputs based on a dimensionality analysis according to the Buckingham Pi theorem enables the reduction of prediction scatter and allows for physical extrapolation. Generally, it is shown that the integration of physics into the data science workflow can enhance prediction performance and generalization, particularly with scarce data and to the extent of physical extrapolation.