Conference Agenda

Idiopathic Pulmonary Fibrosis (IPF) is a disease characterized by the progressive formation of scar tissue in the lungs, leading to locally increased tissue stiffness and impaired respiratory function. To simulate lung behavior, micro-scale and personalizable organ-scale models have recently been developed [1,2,3]. However, integrating these models into a unified multi-scale model that can be personalized based on image data is computationally expensive. In our work, we propose a machine learning-based surrogate modeling framework that could be used to integrate the micro-scale model with the organ-scale model as well as to speed up the personalization procedure.

In this contribution, we investigate the properties of Hierarchical Deep-learning Neural Networks (HiDeNN) [4,5] and introduce several modifications to extend their capabilities [6]. Similar to classical Physics-Informed Neural Networks (PINNs), HiDeNN incorporates knowledge of the underlying physics. However, unlike standard PINNs, the solution is obtained as a linear combination of classical finite element shape functions. Due to their mesh-based structure, HiDeNN models require significantly fewer trainable parameters than fully connected neural networks. Additionally, individual weights and biases have a clear interpretation, which can be leveraged during training.

We compare two approaches to shape function construction: the interpolation-layer-based approach and the reference-element-based approach. In our analysis of model properties, we investigate the impact of different loss functions on training efficiency and solution accuracy, as well as the effect of various numerical integration methods for loss evaluation. Furthermore, we introduce two key extensions to the existing HiDeNN framework: rh-adaptivity, which employs a Jacobian-based criterion to guide adaptive mesh refinement, and a multi-level training strategy that leverages the model’s interpretability to enhance accuracy and computational efficiency. The framework's capabilities are demonstrated on 1D, 2D, and 3D test cases.

[1] Patte, C., Brillet, P.-Y., Fetita, C., Bernaudin, J.-F., Gille, T., Nunes, H., Chapelle, D., and Genet, M. (2022a). Estimation of regional pulmonary compliance in idiopathic pulmonary fibrosis based on personalized lung poromechanical modeling. Journal of Biomechanical Engineering, 144(9):091008.

[2] Patte, C., Genet, M., and Chapelle, D. (2022b). A quasi-static poromechanical model of the lungs. Biomechanics and Modeling in Mechanobiology, 21(2):527–551.

[3] Genet, M., Manoochehrtayebi, M., & Bel-Brunon, A. (2023, October). A micro-poro-mechanical model of the lung parenchyma. In SB 2023-48ème Congrès de la Société de Biomécanique.

[4] Zhang, L., Cheng, L., Li, H., Gao, J., Yu, C., Domel, R., Yang, Y., Tang, S., Liu, W.K., 2021. Hierarchical deep-learning neural networks: finite elements and beyond. Computational Mechanics 67, 207–230.

[5] Zhang, L., Lu, Y., Tang, S., Liu, W.K., 2022. HiDeNN-TD: reduced-order hierarchical deep learning neural networks. Computer Methods in Applied Mechanics and Engineering 389, 114414.

[6] Škardová, K., Daby-Seesaram, A., & Genet, M. (2024). Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs. arXiv preprint arXiv:2412.05719.

The remarkable properties of spider silk, including supercontraction - a significant shrinkage upon wetting - are deeply rooted in the molecular structure of its proteins. Understanding how the primary sequences of silk proteins influence macroscopic fiber behavior is essential for advancing biomimetic materials. In this work, we enhance a previously proposed microstructure-inspired multiscale model for predicting the spider silk supercontraction, by integrating new insights from data-driven modeling [1].

Specifically, by using Evolutionary Polynomial Regression (EPR), a machine learning technique combining genetic programming with symbolic regression, we investigate the relationships between the molecular composition of the silk main proteins and the fiber supercontraction response. Our analysis based on a recent multiscale experimental data across different silk types [2] identifies key sequence motifs: the repeat length of MaSp2 and the polyalanine regions of MaSp1 emerge as fundamental determinants of supercontraction dynamics. EPR generates interpretable mathematical relationships linking these sequence features to fiber contraction, which we interpret in mechanical terms. We propose that the polyalanine domains of MaSp1 regulate β-sheet misalignment, accommodating the shortening of softer regions during supercontraction. Meanwhile, the repeat length of MaSp2 governs the cross-linking interactions that stabilize amorphous chains in the dry state, while hydration disrupts them and triggers macroscopic fiber contraction.

Validation against experimental data from the Silkome database confirms the predictive capability of the proposed model, bridging molecular-scale protein structure with macroscopic fiber behavior. This work offers new insights into the molecular basis of supercontraction and provides a framework for designing biomimetic silk materials with tunable properties.

[1] Fazio, V., Malay, A. D., Numata, K., Pugno, N. M., & Puglisi, G. (2024). A Physically‐Based Machine Learning Approach Inspires an Analytical Model for Spider Silk Supercontraction. Advanced Functional Materials, 2420095.

[2] Arakawa, K., Kono, N., Malay, A. D., Tateishi, A., Ifuku, N., Masunaga, H., ... & Numata, K. (2022). 1000 spider silkomes: Linking sequences to silk physical properties. Science advances, 8(41), eabo6043.

There have been impressive advancements in the application of physics to the modelling of complex cardio-physiological systems, including the dynamics of the blood flow-pressure dependence in the vasculature connected to the heart. In principle this affords opportunities for deeper insight into the nature, cause and best treatment of cardio-physiological diseases. However, the corresponding mathematical models typically do not accommodate closed form solutions and entirely rely on numerical simulation procedures instead. This becomes problematic in clinical applications, where model calibration and patient specific parameter estimation are indispensable, calling for repeated forward simulations from the model as part of an iterative optimisation or sampling procedure at substantial computational costs. A potential workaround is to rely on surrogate models which approximate the simulations. The present work introduces an efficient method of predicting fluid dynamics in systemic arterial networks via physics-informed neural networks. In particular, we explore predictions associated with a 1D-fluid dynamics network model that accepts biophysical parameters as inputs, and as such functions as a surrogate model for numerical solvers of the fluid dynamics problem. The focus of our work lies on patient-specific modelling and requires a ventricular geometry profile as well as blood flow measurements in the ascending aorta which define the inlet boundary condition. Once fully trained, the machine learning model predicts blood flow and pressure waveforms in a fraction of the time taken by the numerical solver, allowing for fast uncertainty quantification of the parameters in the system given observational data using Markov chain Monte Carlo. Our inference framework is applied to magnetic resonance imaging (MRI) and magnetic resonance angiography (MRA) data from four patients diagnosed with double outlet right ventricle (DORV), a congenital heart defect where both the aorta and pulmonary artery originate from the right ventricle, instead of the left and right ventricle respectively. We show that our method provides an accurate non-invasive method of predicting blood pressure in the arteries surrounding the heart, accounting for uncertainty in inferred physiological parameters.