The coupled ghost and gluon Dyson--Schwinger equations (DSEs) of four-dimensional Landau-gauge Yang--Mills (YM) theory are solved with a neural representation trained only from renormalized equation residuals. The neural and fixed-point solutions agree at the percent level and remain stable under changes of initialization, network size, integration grid, and infrared boundary condition. Variations of the three-gluon vertex model produce substantially larger effects than the neural error. The MiniMOM ultraviolet running and the sign change of the gluon Schwinger function are also reproduced within the limitations of the truncation.
Simulation-based inference (SBI) with machine learning is an increasingly important tool for solving inverse problems in science and engineering, including parameter inference and the inversion of detector effects. We provide an overview of the Bayesian and frequentist statistica…
Estimating contemporaneous bidirectional interactions from observational data is difficult because each outcome is endogenous to the other, while flexible regressions may capture only reduced-form dependence. This paper proposes SEM-DNN, a heteroscedastic neural simultaneous-equa…
PDE discovery from sparse observations requires reconstructing a continuous field and selecting the correct differential terms. Our analysis of optimization paths in coupled neural PDE discovery reveals three behaviors: the exact support can persist to the end of training, appear…
Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but this autoregressive rollout feeds every prediction error back as input, so local errors accumulate. E…
We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timeste…
Neural network compression and interpretability remain open challenges in modern deep learn- ing, where billion-parameter architectures deliver impressive accuracy at the cost of trans- parency, computational efficiency, and reliable uncertainty quantification. This paper introdu…