arXiv subjects

David Michael Riley

Publications and source records attributed to David Michael Riley.

3 recordsLinked to original sources

arXiv2026

A shifted interface approach for internal discontinuities in poroelastic media

Porous media containing cracks, fractures, or internal discontinuities arise throughout subsurface geomechanics, biomechanics, and materials science. Numerical simulation of the coupled hydromechanical response is inherently challenging because the pressure and displacement fields are tightly coupled through the Biot equations, requiring stable mixed formulations. These difficulties are compounded when cracks are present, because standard mesh-conforming approaches require costly, labor-intensive, body-fitted meshing, while unfitted methods often require cut-cell integration, enrichment functions, or additional stabilization. In this work, we use an alternative approach, we adapt the shifted interface method to coupled transient poroelasticity with embedded interfaces. The method replaces the true crack by a surrogate approximation where interface conditions are transferred through local expansions. A unified derivation yields shifted forms for both hydraulic transmission and mechanical traction coupling. Two enforcement strategies are extensively compared: a weak (integral) enforcement and a strong (pointwise) enforcement. Four test cases of increasing geometric complexity (offset mesh-aligned, boundary-intersecting angled, embedded angled, and multi-crack configurations) validate the formulation. Away from crack tips, interface residuals converge as O(h); near tips, localized post-processing artifacts degrade the global rate, but first-order convergence is recovered when a small tip region is excluded. A multi-crack demonstration with four simultaneously embedded cracks of distinct geometry and interface properties confirms the practical applicability of the framework. These results support the shifted interface method as a practical framework for poroelastic crack modeling on non-body-fitted meshes with geometrically complex embedded interfaces.

cs.CE↗

arXiv2025

Slip, Differentiate, Observe: State and Parameter Estimation for Rate and State Friction from Noisy Data

Quantifying frictional properties of interfaces remains a major challenge in both terrestrial and extraterrestrial geomechanics, where available samples, laboratory apparatuses, and geophysical observations are inherently limited. We introduce an analytic and numerical framework, grounded in nonlinear control theory, to infer the emergent frictional behavior of seismic faults. From noisy slip measurements, we first reconstruct the slip rate and frictional response in finite time using a Robust Exact Filtering Differentiator (REFD) that attenuates measurement noise. Building on these reconstructions, we design an exponentially convergent adaptive-gain observer that estimates the internal state variable and the key parameters (a - b) and dc of the rate-and-state friction (RSF) law, widely used in fault mechanics. Numerical experiments show that, in fast slip regimes where data are sufficiently rich, the method recovers RSF parameters with errors on the order of 20% and accurately tracks the RSF state variable despite noise contamination, whereas slowly varying sliding periods lack the observability required for reliable estimation. We also establish observability and identifiability conditions for the extended system, enabling the determination of additional parameters and outlining pathways for more advanced control-theoretic approaches to friction and state identification in fault systems. Although we apply the approach to a reduced spring-slider analogue, it improves on classical RSF calibration methods that depend on laboratory access to shear and normal stress. It also offers convergence guarantees and explicit error bounds, and it can further support model-based inversions that embed RSF in forward simulations.

physics.geo-ph↗

arXiv2025

Reinforcement learning-based adaptive time-integration for nonsmooth dynamics

Numerical time integration is fundamental to the simulation of initial and boundary value problems. Traditionally, time integration schemes require adaptive time-stepping to ensure computational speed and sufficient accuracy. Although these methods are based on mathematical derivations related to the order of accuracy for the chosen integrator, they also rely on heuristic development to determine optimal time steps. In this work, we use an alternative approach based on Reinforcement Learning (RL) to select the optimal time step for any time integrator method, balancing computational speed and accuracy. To explore the potential of our RL-based adaptive time-stepping approach, we choose a challenging model problem involving set-valued frictional instabilities at various spatiotemporal scales. This problem demonstrates the robustness of our strategy in handling nonsmooth problems, which present a demanding scenario for numerical integration. Specifically, we apply RL to the simulation of a seismic fault with Coulomb friction. Our findings indicate that RL can learn an optimal strategy for time integration, achieving up to a fourfold speed-up. Our RL-based adaptive integrator offers a new approach for time integration in various other problems in mechanics.

physics.comp-ph↗