Marc Rameaux, an AI specialist and regular contributor to The European Scientist, sees Yann LeCun as the David Hume of our time. Tracing the career of the pioneer of convolutional neural networks, fro...

Level-wise statistical methods for fuzzy random variables, implementing the Puri-Ralescu framework. Provides level-wise empirical distribution functions, moments, covariance and correlation, a level-wise Kolmogorov-Smirnov goodness-of-fit test, an approximate fuzzy normal distribution with simulation, and level-wise central limit theorem and law of large numbers inference. The package only depends on base R.

State inference and parameter learning for nonlinear filters is a core computation for scientific machine learning with varied applications in engineering and neuroscience. The unnormalized filtering distribution is governed by the Zakai equation, a stochastic partial differential equation (SPDE) that combines the forward Kolmogorov operator (known as the Fokker-Planck equation) with observed likelihood updates. Although solving these high-dimensional SPDEs is often impossible analytically and intractable numerically, advances in operator learning and physics-informed machine learning have made it feasible. Harnessing these advances, we introduce the Zakai Equation Neural Operator (ZENO), a model that optimizes a neural operator against a Zakai Equation based physics-informed loss to approximate the exact unnormalized filtering distribution for latent stochastic dynamical systems. We use this ZENO-inferred posterior distribution in an expectation-maximization (EM) framework to perform

Level-wise statistical methods for fuzzy random variables, implementing the Puri-Ralescu framework. Provides level-wise empirical distribution functions, moments, covariance and correlation, a level-wise Kolmogorov-Smirnov goodness-of-fit test, an approximate fuzzy normal distribution with simulation, and level-wise central limit theorem and law of large numbers inference. The package only depends on base R.