arXiv subjects

Ado Farsi

Publications and source records attributed to Ado Farsi.

3 recordsLinked to original sources

arXiv2026

Shape optimisation of nonlinear Naghdi shells on discrete geometries

A thin shell carries load through its shape and, at finite deflections, its stiffness changes with the load itself, so a shape optimum found with a linear model can be far from optimal. We present an automated framework that embeds the fully geometrically nonlinear shell response in the shape-optimisation loop. The forward model, a five-parameter nonlinear Naghdi shell stabilised against locking by partial selective reduced integration, operates directly on a discrete (faceted) triangulation with a numerically recovered director field -- dispensing with the exact mid-surface parameterisation of isogeometric approaches, a chart that ceases to exist once the geometry itself is the design variable. Implemented in Firedrake, the model generates its residual, consistent tangent and adjoint automatically; shape derivatives, computed by algorithmic differentiation through the full load-continuation solve, drive the Fireshape/ROL trust-region optimiser. The forward solver reproduces the Sze/Abaqus benchmark for a clamped semi-cylindrical shell under a point load, capturing the progressive stiffening that a geometrically linear model cannot reproduce. The optimisation is validated against the COMSOL benchmark, a sheet-metal bracket under bending: the framework develops the same off-mid-plane corrugation mechanism and attains an 87% reduction of elastic strain energy within the prescribed displacement budget, matching the benchmark's magnitude and area change. Applied to the curved semi-cylinder, it forms a smooth stiffening crease that reduces the shell's average deflection under load by 78%.

math.NA↗

arXiv2025

Missing Physics Discovery through Fully Differentiable Finite Element-Based Machine Learning

Modelling physical systems with partial differential equations (PDEs) is central to science and engineering, yet in most real applications the PDE model is incomplete: relationships such as constitutive or thermal laws are unknown. Existing surrogate approaches close this gap by learning the PDE solution from data, but remain tied to a specific configuration (geometry, boundary conditions, discretisation) and recover the solution rather than the missing physics itself. We introduce FEML, an end-to-end differentiable framework that couples the known PDE with a machine-learned operator for the missing physics. Embedding the PDE solver into training lets this operator be learned directly from the PDE solution, even when its own output cannot be measured - for example, stress in constitutive laws. Because the operator is independent of the system configuration, a law learned in one setting transfers zero-shot to new geometries, boundary conditions, and discretisations, and can be inspected by domain specialists. FEML represents the operator with structure-preserving operator networks (SPONs), which retain key continuous properties at the discrete level. We demonstrate FEML across solid mechanics and thermal transport. From synthetic data we progressively discover an elastoplastic law - the nonlinear elastic response, then the plastic hardening law - and compose them into a foundation constitutive model that transfers zero-shot to a 3D torsion problem. Moving to real data, we learn coupled plastic-hardening and ductile-damage laws from a benchmark shear-coupon test, reproducing the measured response, including post-peak softening, to within the experimental scatter. Finally, we recover a temperature-dependent conductivity from transient heat-flow data and apply symbolic regression to the learned operator to extract a closed-form law matching the ground truth.

cs.CE↗

arXiv2024

Differentiable programming across the PDE and Machine Learning barrier

The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability to discover new physics. Examples include the use of fundamental physical laws as inductive bias to machine learning algorithms, also referred to as physics-driven machine learning, and the application of machine learning to represent features not represented in the differential equations such as closures for unresolved spatiotemporal scales. However, the simulation of complex physical systems by coupling advanced numerics for PDEs with state-of-the-art machine learning demands the composition of specialist PDE solving frameworks with industry-standard machine learning tools. Hand-rolling either the PDE solver or the neural net will not cut it. In this work, we introduce a generic differentiable programming abstraction that provides scientists and engineers with a highly productive way of specifying end-to-end differentiable models coupling machine learning and PDE-based components, while relying on code generation for high performance. Our interface automates the coupling of arbitrary PDE-based systems and machine learning models and unlocks new applications that could not hitherto be tackled, while only requiring trivial changes to existing code. Our framework has been adopted in the Firedrake finite-element library and supports the PyTorch and JAX ecosystems, as well as downstream libraries.

cs.LG↗