We present a novel mathematical model that seeks to capture the key design feature of generative adversarial networks (GANs). Our model consists of two interacting spin glasses, and we conduct an extensive theoretical analysis of the complexity of the model's critical points using techniques from Random Matrix Theory. The result is insights into the loss surfaces of large GANs that build upon prior insights for simpler networks, but also reveal new structure unique to this setting.

Time series forecasting is an important challenge with significant applications in areas such as weather prediction, stock market analysis, scientific simulations and industrial process analysis. In this work, we introduce LMS-AutoTSF, a novel time series forecasting architecture that incorporates autocorrelation while leveraging dual encoders operating at multiple scales. Unlike models that rely on predefined trend and seasonal components, LMS-AutoTSF employs two separate encoders per scale: one focusing on low-pass filtering to capture trends and the other utilizing high-pass filtering to model seasonal variations. These filters are learnable, allowing the model to dynamically adapt and isolate trend and seasonal components directly in the frequency domain. A key innovation in our approach is the integration of autocorrelation, achieved by computing lagged differences in time steps, which enables the model to capture dependencies across time more effectively. Each encoder processes the input through fully connected layers to handle temporal and channel interactions. By combining frequency-domain filtering, autocorrelation-based temporal modeling, and channel-wise transformations, LMS-AutoTSF not only accurately captures long-term dependencies and fine-grained patterns but also operates more efficiently compared to other state-of-the-art methods. Its lightweight design ensures faster processing while maintaining high precision in forecasting across diverse time horizons. The source code is publicly available at \url{http://github.com/mribrahim/LMS-TSF}

Predicting the solubility of given molecules remains crucial in the pharmaceutical industry. In this study, we revisited this extensively studied topic, leveraging the capabilities of contemporary computing resources. We employed two machine learning models: a linear regression model and a graph convolutional neural network (GCNN) model, using various experimental datasets. Both methods yielded reasonable predictions, with the GCNN model exhibiting the highest level of performance. However, the present GCNN model has limited interpretability while the linear regression model allows scientists for a greater in-depth analysis of the underlying factors through feature importance analysis, although more human inputs and evaluations on the overall dataset is required. From the perspective of chemistry, using the linear regression model, we elucidated the impact of individual atom species and functional groups on overall solubility, highlighting the significance of comprehending how chemical structure influences chemical properties in the drug development process. It is learned that introducing oxygen atoms can increase the solubility of organic molecules, while almost all other hetero atoms except oxygen and nitrogen tend to decrease solubility.

The sensitivity of heterogeneous energetic (HE) materials (propellants, explosives, and pyrotechnics) is critically dependent on their microstructure. Initiation of chemical reactions occurs at hot spots due to energy localization at sites of porosities and other defects. Emerging multi-scale predictive models of HE response to loads account for the physics at the meso-scale, i.e. at the scale of statistically representative clusters of particles and other features in the microstructure. Meso-scale physics is infused in machine-learned closure models informed by resolved meso-scale simulations. Since microstructures are stochastic, ensembles of meso-scale simulations are required to quantify hot spot ignition and growth and to develop models for microstructure-dependent energy deposition rates. We propose utilizing generative adversarial networks (GAN) to spawn ensembles of synthetic heterogeneous energetic material microstructures. The method generates qualitatively and quantitatively realistic microstructures by learning from images of HE microstructures. We show that the proposed GAN method also permits the generation of new morphologies, where the porosity distribution can be controlled and spatially manipulated. Such control paves the way for the design of novel microstructures to engineer HE materials for targeted performance in a materials-by-design framework.