We develop a physics-informed neural network (PINN) framework for parameter estimation in fractional-order SEIRD epidemic models. By embedding the Caputo fractional derivative into the network residuals via the L1 discretization scheme, our method simultaneously reconstructs epidemic trajectories and infers both epidemiological parameters and the fractional memory order $α$. The fractional formulation extends classical integer-order models by capturing long-range memory effects in disease progression, incubation, and recovery. Our framework learns the fractional memory order $α$ as a trainable parameter while simultaneously estimating the epidemiological rates $(β, σ, γ, μ)$. A composite loss combining data misfit, physics residuals, and initial conditions, with constraints on positivity and population conservation, ensures both accuracy and biological consistency. Tests on synthetic Mpox data confirm reliable recovery of $α$ and parameters under noise, while applications to COVID-19 show that optimal $α\in (0, 1]$ captures memory effects and improves predictive performance over the classical SEIRD model. This work establishes PINNs as a robust tool for learning memory effects in epidemic dynamics, with implications for forecasting, control strategies, and the analysis of non-Markovian epidemic processes.

Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building upon the Hegselmann-Krause framework and fractional-order difference, a comprehensive model is established that captures the persistent influence of historical information. Through rigorous theoretical analysis, the fundamental properties including convergence and consensus is investigated. The results demonstrate that the proposed model not only maintains favorable convergence and consensus characteristics compared to classical opinion dynamics, but also addresses limitations such as the monotonicity of bounded opinions. This enables a more realistic representation of opinion evolution in real-world scenarios. The findings of this study provide new insights and methodological approaches for understanding opinion formation and evolution, offering both theoretical significance and practical applications.

The theory of homogenization provides a systematic approach to the derivation of macroscale constitutive laws, obviating the need to repeatedly resolve complex microstructure. However, the unit cell problem that defines the constitutive model is typically not amenable to explicit evaluation. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Many viscoelastic and elastoviscoplastic materials are characterized by memory-dependent constitutive laws. In order to amortize the computational investment in finding such memory-dependent constitutive laws, it is desirable to learn their dependence on the material microstructure. While prior work has addressed learning memory dependence and material dependence separately, their joint learning has not been considered. This paper focuses on the joint learning problem and proposes a novel neural operator framework to address it. In order to provide firm foundations, the homogenization problem for linear Kelvin-Voigt viscoelastic materials is studied. The theoretical properties of the cell problem in this Kelvin-Voigt setting are used to motivate the proposed general neural operator framework; these theoretical properties are also used to prove a universal approximation theorem for the learned macroscale constitutive model. This formulation of learnable constitutive models is then deployed beyond the Kelvin-Voigt setting. Numerical experiments are presented showing that the resulting data-driven methodology accurately learns history- and microstructure-dependent linear viscoelastic and nonlinear elastoviscoplastic constitutive models, and numerical results also demonstrate that the resulting constitutive models can be deployed in macroscale simulation of material deformation.

Stagnant weather condition is one of the major contributors to air pollution as it is favorable for the formation and accumulation of pollutants. To measure the atmosphere's ability to dilute air pollutants, Air Stagnation Index (ASI) has been introduced as an important meteorological index. Therefore, making long-lead ASI forecasts is vital to make plans in advance for air quality management. In this study, we found that autumn Ni\~no indices derived from sea surface temperature (SST) anomalies show a negative correlation with wintertime ASI in southern China, offering prospects for a prewinter forecast. We developed an LSTM-based model to predict the future wintertime ASI. Results demonstrated that multivariate inputs (past ASI and Ni\~no indices) achieve better forecast performance than univariate input (only past ASI). The model achieves a correlation coefficient of 0.778 between the actual and predicted ASI, exhibiting a high degree of consistency.

Eye movements read by a new AI application can reveal thoughts, memories, goals -- and brain diseases. A new tool developed at the Kavli Institute for Systems Neuroscience in Norway and described in an article in Nature Neuroscience, predicts gaze direction and eye movement directly from magnetic resonance imaging (MRI) scans. The goal is to make eye tracking diagnostics a standard in brain imaging research and hospital clinics. Whenever you explore an environment or search for something, you scan the scene using continuous rapid eye movements. Your eyes also make short stops to fixate on certain elements of the scene that you want more detailed information about.

This article introduces a neural network-based signal processing framework for intelligent reflecting surface (IRS) aided wireless communications systems. By modeling radio-frequency (RF) impairments inside the "meta-atoms" of IRS (including nonlinearity and memory effects), we present an approach that generalizes the entire IRS-aided system as a reservoir computing (RC) system, an efficient recurrent neural network (RNN) operating in a state near the "edge of chaos". This framework enables us to take advantage of the nonlinearity of this "fabricated" wireless environment to overcome link degradation due to model mismatch. Accordingly, the randomness of the wireless channel and RF imperfections are naturally embedded into the RC framework, enabling the internal RC dynamics lying on the edge of chaos. Furthermore, several practical issues, such as channel state information acquisition, passive beamforming design, and physical layer reference signal design, are discussed.

In this paper we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the corresponding mean-field approximation based on Vlasov-Fokker-Planck-type equations. The disadvantage of memory effects induced by the need to store the local best position is overcome by the introduction of an additional differential equation describing the evolution of the local best. A regularization process for the global best permits to formally derive the respective mean-field description. Subsequently, in the small inertia limit, we compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization (CBO) methods. Several numerical examples illustrate the mean field process, the small inertia limit and the potential of this general class of global optimization methods.