Panos Pantidis

Panos Pantidis, Habiba Eldababy, Christopher Miguel Tagle et al.

In our recently proposed Integrated Finite Element Neural Network (I-FENN) framework (Pantidis and Mobasher, 2023) we showcased how PINNs can be deployed on a finite element-level basis to swiftly approximate a state variable of interest, and we applied it in the context of non-local gradient-enhanced damage mechanics. In this paper, we enhance the rigour and performance of I-FENN by focusing on two crucial aspects of its PINN component: a) the error convergence analysis and b) the hyperparameter-performance relationship. Guided by the available theoretical formulations in the field, we introduce a systematic numerical approach based on a novel set of holistic performance metrics to answer both objectives. In the first objective, we explore in detail the convergence of the PINN training error and the global error against the network size and the training sample size. We demonstrate a consistent converging behavior of the two error types for any investigated combination of network complexity, dataset size and choice of hyperparameters, which empirically proves the conformance of the PINN setup and implementation to the available convergence theories. In the second objective, we establish an a-priori knowledge of the hyperparameters which favor higher predictive accuracy, lower computational effort, and the least chances of arriving at trivial solutions. The analysis leads to several outcomes that contribute to the better performance of I-FENN, and fills a long-standing gap in the PINN literature with regards to the numerical convergence of the network errors while accounting for commonly used optimizers (Adam and L-BFGS). The proposed analysis method can be directly extended to other ML applications in science and engineering. The code and data utilized in the analysis are posted publicly to aid the reproduction and extension of this research.

Diab W. Abueidda, Bilal Ahmed, Panos Pantidis et al.

In agentic scientific machine learning (SciML), large language model (LLM) agents can discover surrogate models and select one by an automated score, typically an error metric. A low error, however, does not establish that the predicted fields satisfy the physics that matter for mechanics, such as boundary conditions, superposition, stiffness scaling, or causality. We introduce Physics-Audited Agentic SciML (PA-SciML), a verification-first workflow for agentic SciML discovery. The workflow fixes a scoring evaluator before search, derives reviewable machine-checkable physics requirements, checks each trained candidate on its outputs, and separately searches prescribed input ranges or measured load-history spans for high-violation cases without reference solution fields. A surrogate is reported as verified only under the stated checks. When enabled, the workflow also adds advisory numerical probes before training and tests one modeling change at a time to record which isolated edits are associated with score gains before reuse. In the reported computational-solid-mechanics numerical examples, the static elasticity run selects a surrogate with lower validation error than the error-only baseline while both selected models pass the common linear-elastic checks. In the transient elastodynamics run, an error-only baseline with similar mean error fails a stricter causality check by responding to future parts of the loading history, while the selected surrogate passes the stated checks. The main distinction is per-candidate physics evidence on predicted fields, not a richer aggregate score.

Panos Pantidis, Fouad Amin, Diab Abueidda et al.

In this paper we demonstrate how the Integrated Finite Element Neural Network (IFENN) framework can effectively model the entire evolution of phase-field fracture, including the initiation and propagation stage, across generalizable geometries. IFENN is a hybrid scheme for coupled computational mechanics problems, tightly coupling a standard FEM solver (mechanical equilibrium) with a pre-trained neural network (coupled field). In this work, the phase-field diffusion equation is approximated with: i) a DeepONet architecture with Kolmogorov-Arnold networks in the trunk and branch (DeepOKAN) for the initiation stage, and ii) a Convolution Neural Network (CNN) for the propagation stage. Both networks are trained only once, on a benchmark geometry, using a purely physics-informed approach based on the maximum strain energy and the phase-field variable. The training process utilizes an extremely small number of training increments and only a limited number of Gauss points that are strategically sampled from the fracture process zone. These features enable a substantial decrease of the offline training cost. To address the extrapolation of the DeepOKAN predictions in regions away from the crack tip during the inference stage, we implement a set of artificial boundary conditions to enforce the near-zero values in the far-field predictions. We showcase the flexibility and numerical accuracy of the proposed methodology across both the training and unseen geometries.