Andrew Franck | Search arXiv

arXiv2026

Fast Surrogate Modeling of Excitable and Oscillatory FitzHugh-Nagumo Dynamics with Parametric Neural Operators

The FitzHugh-Nagumo (FHN) system serves as a simplified model of neuronal voltage dynamics, capturing the activator-inhibitor structure behind both isolated action potentials and the rhythmic spiking seen across the brain. Exploring its 5D physiological parameter space is important for neuromodulation and mapping voltage recordings back to biophysics, yet classical finite-difference solvers make rapid parameter sweeps expensive. We train parameter-conditioned Fourier Neural Operators (FNOs) as fast, differentiable surrogates for the FHN voltage and recovery fields on a one-dimensional spatial domain, conditioning each Fourier layer on the parameter vector $λ= (D_u, D_v, a, b, τ)$ via feature-wise linear modulation (FiLM). We apply a single bifurcation analysis that delimits the two distinct regimes the model spans, oscillatory (tonic firing) and excitable (action-potential propagation), and we train one operator in each. In the oscillatory regime the surrogate attains sub-$0.1\%$ relative $L^2$ error on both fields, runs nearly three orders of magnitude faster than the finite-difference baseline, generalizes uniformly across the parameter space, and extrapolates to low single-digit percentage errors outside of the training bounds. In the excitable regime the same operator accurately reproduces the firing threshold and the $c \propto \sqrt{D_u}$ conduction-velocity law and replicates full traveling pulses, fully capturing the excitable bifurcation structure rather than just smoothly interpolating fields.

cs.LG↗

arXiv2026

VISTA: Dense Multi-Label Classroom Coding with Vision-Language Models

Video-language benchmarks are usually constructed by the dataset authors without published reliability statistics, leaving the noise floor of the construct unknown. We argue that multimodal benchmarking benefits from methods taken from research communities that have already invested in strategies to ensure reliability. We illustrate the case with the Classroom Observation Protocol for Undergraduate STEM (COPUS): a 24-code multi-label observation instrument with a decade of peer-reviewed reliability literature. We recast COPUS as a video benchmark for multimodal foundation models, where it provides a dense set of structured labels (a 24-dimensional binary vector every 2 minutes across a 50-90 minute lecture), an externally validated vocabulary, and established literature that provides a per-code reliability target based on human evaluators. Annotations in our evaluation corpus are produced by a 5-person human-evaluator panel whose consensus matrix is our reference. We propose VISTA, a baseline that runs MiniCPM-V-4.5 over a dense sliding window, refines its per-window outputs with a lightweight multi-layer perceptron (MLP) head trained on top of the frozen backbone, and max-pools the resulting predictions onto the 2-minute COPUS grid. On three held-out chemistry lectures, VISTA reaches 80.1% restricted macro accuracy versus 74.9% for the zero-shot variant, with the largest residual errors on visually similar instructor codes and on rare audio-dependent codes. We characterize three systematic failure modes (audio-partial observability, fine-grained group-work discrimination, long-tail recall) and release the benchmark tooling, prompts and baseline code at https://github.com/ajfranck/VISTA.

cs.CV↗