Mark Wilkinson

Mark Wilkinson, Amirhossein Amiri-Hezaveh, Adrian Buganza Tepole

Soft materials such as rubbers, hydrogels, and biological tissues undergo damage in the form of stiffness degradation without apparent changes in their stress-free geometry. Accurate simulation of this behavior is critical in applications ranging from soft robotics to the design of medical devices, yet two persistent challenges are the difficulty of constructing flexible, thermodynamically consistent constitutive models, and the mesh dependence of finite element solutions caused by strain softening. Here we address both challenges simultaneously by combining physics-augmented neural network constitutive models with a gradient-enhanced damage formulation implemented within the differentiable finite element framework JAX-FEM. The elastic strain energy and the damage yield function are each parameterized by input-convex neural networks (ICNNs), which enforce polyconvexity and satisfaction of the Clausius--Duhem inequality by design. The gradient-enhanced formulation introduces a non-local damage field governed by an additional partial differential equation, regularizing the spatial distribution of damage and eliminating mesh dependence. The implementation is validated through local stress-strain fits, single-element parametric studies, a mesh and solution strategy study for a uniform deformation case, and a notched plate simulation. The results demonstrate that the proposed framework enables flexible, data-driven, mesh-independent damage simulation for a broad class of soft materials. We anticipate that the open-source implementation will lower the barrier to adopting physics-augmented neural network constitutive models.

Julia Navarro, Mark Wilkinson

We construct and evaluate group-equivariant neural networks for the prediction of the two-dimensional $Q$-tensor order parameter of nematic liquid crystals from synthetically generated microscopic textures. Seven architectures, equivariant to cyclic groups $C_k$ of order $k$ for $k=4,\,8,\,16,\,32,\,64,\,128,\, 256$, are built using a combination of weight-sharing constraints, equivariant activations and regularization techniques. To do this, we construct rotation-like permutation matrix groups with elements $\varrho_{C_k}(g)$ that act on row-wise vectorized images, thereby approximating a $\frac{2π}{k}$ rotation of the circular subdomain on square images. We show that all seven equivariant models satisfy the $Q$-tensor equivariance constraint to within single-precision floating point accuracy. Comparing against approximate parameter-matched non-equivariant benchmarks, with and without data augmentation, we find that the equivariant models consistently achieve lower errors and generalize more robustly to unseen defect configurations. Performance increases with group order, suggesting that the incorporation of finer rotational symmetry leads to lower errors.

Ali Zahir, Ashiq Anjum, Mark Wilkinson et al.

The growing complexity and scale of scientific workflows in high performance computing (HPC) environments have led to significant challenges in managing energy consumption without compromising computational performance. Traditional scheduling strategies often fail to account for the complex interplay between thermal dynamics, workload diversity, and system scalability, leading to inefficient and unsustainable energy usage. This paper introduces a novel, scalable, and AI-assisted scheduling framework for optimizing energy consumption in HPC environments without compromising performance. Central to our approach is the integration of Computational Fluid Dynamics (CFD) with a Physics-Informed Variational Autoencoder (PIVAE), enabling the generation of physically realistic synthetic workload data that bridges the gap between thermodynamic behavior and scheduler decision-making in complex, multi-scale HPC environments. By categorizing workflows based on resource utilization profiles, we evaluate multiple scheduling strategies such as Locality Aware and Speculative Aware Scheduling. These workflows, ranging from event reconstruction to anomaly detection, represent diverse computational intensities. Our results show that modest reductions in CPU performance (e.g., to 15%) can yield substantial energy savings (up to 10%) with only minor turnaround time increases (approximately 5-6%), identifying an optimal operational sweet spot. This work demonstrates how physics-informed generative modeling can enable adaptive, sustainable, and data-efficient scheduling for next-generation HPC infrastructures.