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We present a scalable machine learning (ML) force-field model for the adiabatic dynamics of cooperative Jahn-Teller (JT) systems. Large scale dynamical simulations of the JT model also shed light on the orbital ordering dynamics in colossal magnetoresistance manganites. The JT effect in these materials describes the distortion of local oxygen octahedra driven by a coupling to the orbital degrees of freedom of $e_g$ electrons. An effective electron-mediated interaction between the local JT modes leads to a structural transition and the emergence of long-range orbital order at low temperatures. Assuming the principle of locality, a deep-learning neural-network model is developed to accurately and efficiently predict the electron-induced forces that drive the dynamical evolution of JT phonons. A group-theoretical method is utilized to develop a descriptor that incorporates the combined orbital and lattice symmetry into the ML model. Large-scale Langevin dynamics simulations, enabled by the ML force-field models, are performed to investigate the coarsening dynamics of the composite JT distortion and orbital order after a thermal quench. The late-stage coarsening of orbital domains exhibits pronounced freezing behaviors which are likely related to the unusual morphology of the domain structures. Our work highlights a promising avenue for multi-scale dynamical modeling of correlated electron systems.

Reactive transport in porous media plays a pivotal role in subsurface reservoir processes, influencing fluid properties and geochemical characteristics. However, coupling fluid flow and transport with geochemical reactions is computationally intensive, requiring geochemical calculations at each grid cell and each time step within a discretized simulation domain. Although recent advancements have integrated machine learning techniques as surrogates for geochemical simulations, ensuring computational efficiency and accuracy remains a challenge. This chapter investigates machine learning models as replacements for a geochemical module in a reactive transport in porous media simulation. We test this approach on a well-documented cation exchange problem. While the surrogate models excel in isolated predictions, they fall short in rollout predictions over successive time steps. By introducing modifications, including physics-based constraints and tailored dataset generation strategies, we show that machine learning surrogates can achieve accurate rollout predictions. Our findings emphasize that, when judiciously designed, machine learning surrogates can substantially expedite the cation exchange problem without compromising accuracy, offering significant potential for a range of reactive transport applications.

Existing approaches for device placement ignore the topological features of computation graphs and rely mostly on heuristic methods for graph partitioning. At the same time, they either follow a grouper-placer or an encoder-placer architecture, which requires understanding the interaction structure between code operations. To bridge the gap between encoder-placer and grouper-placer techniques, we propose a novel framework for the task of device placement, relying on smaller computation graphs extracted from the OpenVINO toolkit using reinforcement learning. The framework consists of five steps, including graph coarsening, node representation learning and policy optimization. It facilitates end-to-end training and takes into consideration the directed and acyclic nature of the computation graphs. We also propose a model variant, inspired by graph parsing networks and complex network analysis, enabling graph representation learning and personalized graph partitioning jointly, using an unspecified number of groups. To train the entire framework, we utilize reinforcement learning techniques by employing the execution time of the suggested device placements to formulate the reward. We demonstrate the flexibility and effectiveness of our approach through multiple experiments with three benchmark models, namely Inception-V3, ResNet, and BERT. The robustness of the proposed framework is also highlighted through an ablation study. The suggested placements improve the inference speed for the benchmark models by up to $58.2\%$ over CPU execution and by up to $60.24\%$ compared to other commonly used baselines.

We investigate the geometry of a family of log-linear statistical models called quasi-independence models. The toric fiber product is useful for understanding the geometry of parameter inference in these models because the maximum likelihood degree is multiplicative under the TFP. We define the coordinate toric fiber product, or cTFP, and give necessary and sufficient conditions under which a quasi-independence model is a cTFP of lower-order models. We show that the vanishing ideal of every 2-way quasi-independence model with ML-degree 1 can be realized as an iterated toric fiber product of linear ideals. We also classify which Lawrence lifts of 2-way quasi-independence models are cTFPs and give a necessary condition under which a $k$-way model has ML-degree 1 using its facial submodels.

We present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanisms, such as waves, Schr\"odinger equations, and other dispersive models. This framework utilizes the probabilistic setting established by Henry-Labord\`ere and Touzi. We illustrate this approach by providing rigorous bounds on the approximation error for both linear and nonlinear waves in physical dimensions $d=1,2,3$, and analyze their respective computational costs starting from time zero. We investigate two key scenarios: one involving a linear perturbative source term, and another focusing on pure nonlinear internal interactions.

The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we need (1) to elicit a formula for the Fisher-Rao geodesics, and (2) to integrate the Fisher length element along those geodesics. We consider several numerically robust approximation and bounding techniques for the Fisher-Rao distances: First, we report generic upper bounds on Fisher-Rao distances based on closed-form 1D Fisher-Rao distances of submodels. Second, we describe several generic approximation schemes depending on whether the Fisher-Rao geodesics or pregeodesics are available in closed-form or not. In particular, we obtain a generic method to guarantee an arbitrarily small additive error on the approximation provided that Fisher-Rao pregeodesics and tight lower and upper bounds are available. Third, we consider the case of Fisher metrics being Hessian metrics, and report generic tight upper bounds on the Fisher-Rao distances using techniques of information geometry. Uniparametric and biparametric statistical models always have Fisher Hessian metrics, and in general a simple test allows to check whether the Fisher information matrix yields a Hessian metric or not. Fourth, we consider elliptical distribution families and show how to apply the above techniques to these models. We also propose two new distances based either on the Fisher-Rao lengths of curves serving as proxies of Fisher-Rao geodesics, or based on the Birkhoff/Hilbert projective cone distance. Last, we consider an alternative group-theoretic approach for statistical transformation models based on the notion of maximal invariant which yields insights on the structures of the Fisher-Rao distance formula which may be used fruitfully in applications.

Software engineering (SE) activities have been revolutionized by the advent of pre-trained models (PTMs), defined as large machine learning (ML) models that can be fine-tuned to perform specific SE tasks. However, users with limited expertise may need help to select the appropriate model for their current task. To tackle the issue, the Hugging Face (HF) platform simplifies the use of PTMs by collecting, storing, and curating several models. Nevertheless, the platform currently lacks a comprehensive categorization of PTMs designed specifically for SE, i.e., the existing tags are more suited to generic ML categories. This paper introduces an approach to address this gap by enabling the automatic classification of PTMs for SE tasks. First, we utilize a public dump of HF to extract PTMs information, including model documentation and associated tags. Then, we employ a semi-automated method to identify SE tasks and their corresponding PTMs from existing literature. The approach involves creating an initial mapping between HF tags and specific SE tasks, using a similarity-based strategy to identify PTMs with relevant tags. The evaluation shows that model cards are informative enough to classify PTMs considering the pipeline tag. Moreover, we provide a mapping between SE tasks and stored PTMs by relying on model names.

The Log-Periodic Power Law Singularity (LPPLS) model offers a general framework for capturing dynamics and predicting transition points in diverse natural and social systems. In this work, we present two calibration techniques for the LPPLS model using deep learning. First, we introduce the Mono-LPPLS-NN (M-LNN) model; for any given empirical time series, a unique M-LNN model is trained and shown to outperform state-of-the-art techniques in estimating the nonlinear parameters $(t_c, m, \omega)$ of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Second, we extend the M-LNN model to a more general model architecture, the Poly-LPPLS-NN (P-LNN), which is able to quickly estimate the nonlinear parameters of the LPPLS model for any given time-series of a fixed length, including previously unseen time-series during training. The Poly class of models train on many synthetic LPPLS time-series augmented with various noise structures in a supervised manner. Given enough training examples, the P-LNN models also outperform state-of-the-art techniques for estimating the parameters of the LPPLS model as evidenced by the comprehensive distribution of parameter errors. Additionally, this class of models is shown to substantially reduce the time to obtain parameter estimates. Finally, we present applications to the diagnostic and prediction of two financial bubble peaks (followed by their crash) and of a famous rockslide. These contributions provide a bridge between deep learning and the study of the prediction of transition times in complex time series.

Mobile devices and the Internet of Things (IoT) devices nowadays generate a large amount of heterogeneous spatial-temporal data. It remains a challenging problem to model the spatial-temporal dynamics under privacy concern. Federated learning (FL) has been proposed as a framework to enable model training across distributed devices without sharing original data which reduce privacy concern. Personalized federated learning (PFL) methods further address data heterogenous problem. However, these methods don't consider natural spatial relations among nodes. For the sake of modeling spatial relations, Graph Neural Netowork (GNN) based FL approach have been proposed. But dynamic spatial-temporal relations among edge nodes are not taken into account. Several approaches model spatial-temporal dynamics in a centralized environment, while less effort has been made under federated setting. To overcome these challeges, we propose a novel Federated Adaptive Spatial-Temporal Attention (FedASTA) framework to model the dynamic spatial-temporal relations. On the client node, FedASTA extracts temporal relations and trend patterns from the decomposed terms of original time series. Then, on the server node, FedASTA utilize trend patterns from clients to construct adaptive temporal-spatial aware graph which captures dynamic correlation between clients. Besides, we design a masked spatial attention module with both static graph and constructed adaptive graph to model spatial dependencies among clients. Extensive experiments on five real-world public traffic flow datasets demonstrate that our method achieves state-of-art performance in federated scenario. In addition, the experiments made in centralized setting show the effectiveness of our novel adaptive graph construction approach compared with other popular dynamic spatial-temporal aware methods.

In software practice, static analysis tools remain an integral part of detecting defects in software and there have been various tools designed to run the analysis in different programming languages like Java, C++, and Python. This paper presents an empirical comparison of popular static analysis tools for identifying software defects using several datasets using Java, C++, and Python code. The study used popular analysis tools such as SonarQube, PMD, Checkstyle, and FindBugs to perform the comparison based on using the datasets. The study also used various evaluation metrics such as Precision, Recall, and F1-score to determine the performance of each analysis tool. The study results show that SonarQube performs considerably well than all other tools in terms of its defect detection across the various three programming languages. These findings remain consistent with other existing studies that also agree on SonarQube being an effective tool for defect detection in software. The study contributes to much insight on static analysis tools with different programming languages and additional information to understand the strengths and weaknesses of each analysis tool. The study also discusses the implications for software development researchers and practitioners, and future directions in this area. Our research approach aim is to provide a recommendation guideline to enable software developers, practitioners, and researchers to make the right choice on static analysis tools to detect errors in their software codes. Also, for researchers to embark on investigating and improving software analysis tools to enhance the quality and reliability of the software systems and its software development processes practice.