A deep learning approach to the measurement of long-lived memory kernels from generalized Langevin dynamics

Probing intrinsic noise correlation time in non-Markovian diffusive systems

The generalized Langevin equation describes molecular motion in complex systems using memory and random noise terms. Memory effects, the inherent time correlation in random noise, significantly influence molecular diffusive behaviors. However, estimating the intrinsic noise correlation time remains challenging because of difficulties in measuring the memory term. We propose a metric to probe the noise correlation time based on the deviation between characteristic times of configurational diffusion and "diffusion motion" in the kinetic energy space. This approach stems from the observation that memory effects delay relaxation time between displacement and velocity response functions. Our metric relies solely on the velocity autocorrelation function, commonly used in experimental model parameterization. Both analytical and numerical results for various physical models demonstrate its effectiveness in probing noise correlation time. Furthermore, we apply this metric to study complex diffusive phenomena, including non-exponential relaxation in molecular hydrodynamics and anomalous diffusion in crowded environments. By comparing with system's relaxation time, we reveal that long-range noise correlations play a key role in these non-trivial diffusive phenomena.

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.