Nacime Bouziani

Ado Farsi, Nacime Bouziani, David A Ham

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.

Nacime Bouziani, David A. Ham

Partial differential equations (PDEs) are central to describing and modelling complex physical systems that arise in many disciplines across science and engineering. However, in many realistic applications PDE modelling provides an incomplete description of the physics of interest. PDE-based machine learning techniques are designed to address this limitation. In this approach, the PDE is used as an inductive bias enabling the coupled model to rely on fundamental physical laws while requiring less training data. The deployment of high-performance simulations coupling PDEs and machine learning to complex problems necessitates the composition of capabilities provided by machine learning and PDE-based frameworks. We present a simple yet effective coupling between the machine learning framework PyTorch and the PDE system Firedrake that provides researchers, engineers and domain specialists with a high productive way of specifying coupled models while only requiring trivial changes to existing code.

Nacime Bouziani, Shubhi Tyagi, Joseph Fisher et al.

Extracting structured information from unstructured text is critical for many downstream NLP applications and is traditionally achieved by closed information extraction (cIE). However, existing approaches for cIE suffer from two limitations: (i) they are often pipelines which makes them prone to error propagation, and/or (ii) they are restricted to sentence level which prevents them from capturing long-range dependencies and results in expensive inference time. We address these limitations by proposing REXEL, a highly efficient and accurate model for the joint task of document level cIE (DocIE). REXEL performs mention detection, entity typing, entity disambiguation, coreference resolution and document-level relation classification in a single forward pass to yield facts fully linked to a reference knowledge graph. It is on average 11 times faster than competitive existing approaches in a similar setting and performs competitively both when optimised for any of the individual subtasks and a variety of combinations of different joint tasks, surpassing the baselines by an average of more than 6 F1 points. The combination of speed and accuracy makes REXEL an accurate cost-efficient system for extracting structured information at web-scale. We also release an extension of the DocRED dataset to enable benchmarking of future work on DocIE, which is available at https://github.com/amazon-science/e2e-docie.

Nacime Bouziani, David A. Ham, Ado Farsi

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.