Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design

Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding mechanistic differential equations into neural network training, enabling interpretable constitutive operators to be recovered directly from sparse and noisy observations. However, reliable operator recovery depends sensitively on network architecture, optimisation strategy, and data informativeness. Here, we present a systematic empirical study of how these factors influence mechanistic inference using BINNs applied to canonical one-dimensional advection-diffusion-reaction partial differential equation models. Across a suite of benchmark problems, we investigate how network expressivity, learning rate, loss weighting, and batch size influence optimisation behaviour and operator recovery. We show that successful mechanistic inference depends on balancing competing objectives rather than maximising any single aspect of the model or optimisation. Moderately expressive architectures outperform overly complex networks, intermediate learning rates improve optimisation stability, balanced data and PDE losses are essential for accurate operator recovery, and intermediate batch sizes provide the best compromise between computational efficiency and reproducibility. We further identify practical diagnostics for recognising common failure modes, including over-fitting, unstable optimisation, and poor mechanistic recovery when the ground truth is unavailable. Together, these findings provide evidence-based guidelines for deploying BINNs as credible tools for biological model discovery.

How Can AI Find My Model? A Model-Finding Experimental Study Considering Data Formats, Embeddings, and Retrieval Strategies

Discovering simulation models for reuse remains a fundamental challenge in Modeling and Simulation (M&S). When many models coexist, identifying those that align with a given modeling intent remains difficult. Recent advances in Artificial Intelligence (AI), particularly retrieval-based approaches, offer a promising pathway to operate at this semantic layer. In this paper, we present an experimental study investigating the impact of data representation, transformer-based embedding models, and retrieval strategies on the discovery of simulation models using natural language queries. We evaluated performance across multiple query types using standard information retrieval metrics, including recall@5 and nDCG@5. Results show that data representation matters, open-source embedding models can achieve high performance, and reranking methods are important, especially as query complexity increases. This work provides a baseline for AI-driven model discovery and discusses its role in advancing toward AI-driven composability and interoperability.

Think-Aloud Reshapes Automated Cognitive Model Discovery Beyond Behavior

Computational cognitive models discovered using large language models have so far relied solely on behavioral data. However, it is well-known that models produced from the behavioral trajectory alone are typically under-determined. In this work, we explore the use of Think Aloud traces as an additional form of data constraint during automated model discovery. When applied to the domain of risky decision-making, we find that the models discovered with think-aloud achieve significantly improved predictive performance on held-out data. Additionally, we find that the discovered models belong to different structural classes than those discovered from behavior alone for the majority of participants (69.4\%), specifically, it shifts from Explicit comparator towards Integrated utility. These results suggest that process-level language data not only improve model fit, but also systematically reshape the structure of the discovered cognitive models, enabling the identification of mechanisms that are not recoverable from behavior alone.

A Continuous-Time Ensemble Kalman-Bucy Smoother for Causal Inference and Model Discovery

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an uncertainty reduction beyond the filter. This paper introduces an ensemble Kalman-Bucy smoother (EnKBS) for continuous-time DA of nonlinear dynamical systems, where the smoother's conditional distributions are reconstructed using ensemble moments. The result is a derivative-free framework that does not require explicit computation of tangent-linear or adjoint models, which converges to the exact smoother solution at the infinite-ensemble limit for a wide class of complex systems. Incorporating standard regularization techniques for high-dimensional systems, such as covariance localization and inflation, the skill of the EnKBS is demonstrated in various important scientific problems. By integrating future observations, which reveal the underlying causal mechanisms for retrospective state updates, the EnKBS is used for Bayesian-based inference of causal relationships and their temporal influence range in a dyadic trigger-feedback model and the development of a causality-driven iterative learning algorithm that identifies the structure and recovers the hidden parameters of a nonlinear reduced-order model mimicking midlatitude atmospheric circulation. Notably, both tasks remain effective with an ensemble size of $O(10)$ under partial observations, suggesting that EnKBS can support the instantaneous discovery of high-dimensional complex systems over time.