Source Code for KESS-Regularized DeepONets: Enforcing Algebraic Closure Invariants in Neural Operators for Driven Aggregation–Fragmentation Kinetics

This repository contains the PyTorch implementation of the KESS-regularized DeepONet and a numerical verification script. KESSLoss adds to the training objective a penalty on violations of an exact linear recurrence satisfied by the driven constant-kernel steady state, with the aim of reducing tail hallucination when extrapolating beyond the supervised range. The verification script checks the closed-form steady state and the recurrence invariant at 50-digit precision, and the model and loss implementation in double precision (17 checks in total). The training experiment reported in the accompanying paper (5 random seeds) is exploratory: it suggests a stabilizing effect on tail extrapolation, with p = 0.15 for the accuracy gain and p = 0.25 for the variance reduction.

This software accompanies the preprint "KESS-Regularized DeepONets: Enforcing Algebraic Closure Invariants in Neural Operators for Driven Aggregation–Fragmentation Kinetics", available on SSRN at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=7538799.