A Physics-Informed Neural Network framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure is introduced.
Abstract
Tumor progression is an inherently multiphysical phenomenon in which interstitial fluid dynamics, biochemical transport, and cellular mechanics interact across multiple spatiotemporal scales. Classical mesh-based solvers, although accurate, impose prohibitive computational costs for the repeated evaluations demanded by inverse parameter identification and future patient-specific predictive pipelines. In this work we introduce a Physics-Informed Neural Network (PINN) framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure. By intentionally decoupling the solid-mechanical equilibrium, we obtain a three-equation system whose gradient structure is stable under automatic differentiation, enabling robust deep-learning optimization. The network simultaneously learns both state variables from physics constraints alone (forward problem) and recovers hidden transport parameters from sparse, noisy synthetic measurements (Data-Assimilation PINN, DA-PINN, inverse problem). We verify the forward solver against a high-resolution finite-difference (FD) reference, achieving a mean absolute error below 0.002. For the inverse problem, starting from an initial permeability estimate of 0.08 (a factor of 4x above the true value of 0.02) with only 5% spatially sparse observations corrupted by 5% Gaussian noise, the DA-PINN recovers the permeability with a relative error below 5%. These results demonstrate that physics-informed deep learning constitutes a viable, computationally efficient route to multiphysics oncology modeling and lays the mathematical groundwork for future integration into clinical data assimilation pipelines.
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hai-Long Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
The growing application of physics-informed neural networks (PINNs) for solving parametric partial differential equations (PDEs) in fluid dynamics has demonstrated their potential for modeling complex multiscale flows; however, conventional PINNs often exhibit spectral bias and slow, unstable convergence, limiting accuracy in boundary layers and wakes. This research presents novel physics-informed feature decomposition in residual dense block neural networks (PI-RDB-NN), which embeds physical constraints directly into the network architecture rather than relying solely on soft constraints. PI-RDB-NN uses hierarchical residual dense blocks for multi-scale feature extraction, allocates feature channels to velocity and pressure in a 2:1 ratio consistent with two-dimensional incompressible Navier–Stokes physics, and enforces mass conservation via a learnable divergence-aware projection applied at the feature level. The model is evaluated on National Advisory Committee for Aeronautics (NACA) 0012 airfoil flow at Reynolds numbers (Re)=5000 and Re=1000 using a hybrid loss combining PDE residuals, boundary conditions, and sparse computational fluid dynamics (CFD) data. PI-RDB-NN reduces PDE residual and divergence error by 91.2% and 71.7% vs traditional PINNs (Re=5000) and by 85.5% and 85.4% vs a physics-informed Deep Operator Network (DeepONet) baseline (Re=1000). These physics consistency gains improve aerodynamic force predictions and CFD agreement, confirmed by velocity, wake, and pressure coefficient (Cp) distributions. Consistent accuracy across both Reynolds regimes supports the framework's generality, with three-dimensional and unsteady extensions identified as future work.
Sarmad Iftikhar, Ishfaq Ahmad, Diltaj Ali et al.· The Physics of Fluids· 0 citations
The results demonstrate that the mPINN architecture functions as a reliable, physics-constrained ML framework capable of delivering high-fidelity trajectory predictions for complex multi-body molecular systems.
T. Muther, Vuong Van Pham, A. K. Dahaghi· Machine Learning: Science an...· 0 citations
The integration of deep learning with partial differential equation (PDE) solvers has emerged as a transformative paradigm in computational science, offering unprecedented capabilities for modeling complex biophysical systems. This paper presents a comprehensive framework for PDE solvers enhanced by deep learning, specifically tailored for genomic fluid dynamics applications. We propose a hybrid architecture combining Physics-Informed Neural Networks (PINNs) with operator learning techniques to efficiently solve nonlinear PDEs governing blood flow in viscoelastic arteries, with emphasis on the influence of external magnetic fields and genomic-scale parameter variations. Our methodology leverages the complementary strengths of neural networks and physics-based constraints, enabling accurate prediction of pressure and radius disturbances in arterial fluid flow while maintaining computational efficiency. The framework incorporates symbolic regression for model interpretability and demonstrates superior performance compared to conventional numerical solvers across multiple test cases. Experimental results indicate that our approach achieves up to 85% reduction in computational time while maintaining solution accuracy within 2% error margins. This research contributes to the growing field of scientific machine learning by providing a robust, interpretable, and efficient solution for genomic fluid dynamic simulations with potential applications in personalized medicine and biomedical device design.
C. Manigandan, S. Jeyarani, S.Selvakumar et al.· International journal of com...· 0 citations
Physics-Informed Neural Networks (PINNs) have recently gained considerable attention as a mesh-free framework for solving partial differential equations. Nevertheless, their performance deteriorates when applied to strongly coupled multiphysics systems, such as Biot's consolidation model, due to severely ill-conditioned optimization landscapes. In this work, we propose a robust PINN-based solver, termed FS-ENGD-PINN, which synergistically integrates physics-based decoupling with geometry-aware optimization. Specifically, the Fixed-Stress (FS) splitting scheme is employed to decompose the coupled poroelastic system into contractive mechanics and flow subproblems, thereby significantly improving training stability and convergence. To further accelerate optimization, we adopt Energy Natural Gradient Descent (ENGD), which approximates the Newton direction in function space effectively mitigates stiffness-induced slow convergence. Moreover, to address volumetric locking arising in the nearly incompressible regime, we incorporate a three-field mixed formulation with an additional total pressure variable into the PINN framework. Extensive numerical experiments demonstrate that the proposed FS-ENGD-PINN consistently outperforms standard PINN formulations in terms of accuracy and robustness, providing a unified and reliable learning-based solver for poroelasticity across a wide range of material parameters.
Kexin Sun, Qiang Liu, Ming-Cheng Feng et al.· 0 citations
Grid-based fluid dynamics solvers routinely struggle with exhaustive meshing demands and ill-posed inverse problems. A practical mesh-free alternative is given by Physics-informed neural networks (PINNs) but, applying them to highly elastic Oldroyd-B fluids results in many training failures. The High Weissenberg Number Problem (HWNP), driven by the exponential stress growth near stagnation points is a major issue, which causes standard PINN optimizers to diverge. To prevent the network from crashing, we apply a Cholesky decomposition to the conformation tensor. This mathematical constraint stabilizes the gradients by guaranteeing a positive-definite stress field. Beyond mathematical stability, the inherent spectral bias of deep learning models can hinder the network from accurately capturing the highly elastic wake structures. Therefore, we used sparse data assimilation to force the model toward the actual physical solution. By anchoring the physics loss with targeted CFD data points and accelerating training via transfer learning, we successfully pushed the network past non-physical local minima. We validated this Cholesky-PINN approach on flow past cylindrical geometries for Reynolds numbers (Re) between 5-25, for the single-cylinder setup. In addition, the relaxation time ({\lambda}) is increased from 0.1 to 0.5 to test the stability of the network. Finally, we scale the framework to a complex 3-cylinder array which proved our constructive solid geometry approach completely bypasses the tedious re-meshing steps of traditional CFD. The combined framework accurately captured sharp viscoelastic wakes, providing a stable computational tool for complex rheological modeling.
Unknown authors· 0 citations
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