We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems, including reaction-diffusion systems, and forced and unforced Navier-Stokes equations. When compared to numerical solvers of the same accuracy, our method demonstrates a 10 increase in performance speed. Partial differential equations (PDEs) are fundamental for describing complex systems like turbulent flow (Temam, 2001), diffusive processes (Friedman, 2008), and thermodynamics (Van Kampen, 1992). Due to their complexity, these systems frequently lack closed-form analytical solutions, prompting the use of numerical methods. These numerical techniques discretize the spatiotemporal domain of interest and solve a set of discrete equations to approximate the system's behavior. Spectral methods are one such class of numerical techniques, and are widely recognized for their effectiveness (Boyd, 2001; Gottlieb & Orszag, 1977).

This chapter is a preprint from our book by , focusing on leveraging machine learning (ML) in chemical and polyolefin manufacturing optimization. It's crafted for both novices and seasoned professionals keen on the latest ML applications in chemical processes. We trace the evolution of AI and ML in chemical industries, delineate core ML components, and provide resources for ML beginners. A detailed discussion on various ML methods is presented, covering regression, classification, and unsupervised learning techniques, with performance metrics and examples. Ensemble methods, deep learning networks, including MLP, DNNs, RNNs, CNNs, and transformers, are explored for their growing role in chemical applications. Practical workshops guide readers through predictive modeling using advanced ML algorithms. The chapter culminates with insights into science-guided ML, advocating for a hybrid approach that enhances model accuracy. The extensive bibliography offers resources for further research and practical implementation. This chapter aims to be a thorough primer on ML's practical application in chemical engineering, particularly for polyolefin production, and sets the stage for continued learning in subsequent chapters. Please cite the original work [169,170] when referencing.

Recent models have achieved human level performance on the Stanford Question Answering Dataset when using F1 scores to evaluate the reading comprehension task. Yet, teaching machines to comprehend text has not been solved in the general case. By appending one adversarial sentence to the context paragraph, past research has shown that the F1 scores from reading comprehension models drop almost in half. In this paper, I replicate past adversarial research with a new model, ELECTRA-Small, and demonstrate that the new model's F1 score drops from 83.9% to 29.2%. To improve ELECTRA-Small's resistance to this attack, I finetune the model on SQuAD v1.1 training examples with one to five adversarial sentences appended to the context paragraph. Like past research, I find that the finetuned model on one adversarial sentence does not generalize well across evaluation datasets. However, when finetuned on four or five adversarial sentences the model attains an F1 score of more than 70% on most evaluation datasets with multiple appended and prepended adversarial sentences. The results suggest that with enough examples we can make models robust to adversarial attacks.

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from $\mathcal{O}(L^6)$ to $\mathcal{O}(L^3)$, where $L$ is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

Possible unfavourable scenarios span from excess water inflow or a damaging of the Tunnel Boring Machine (TBM) to a total collapse of the tunnel [1]. To avoid potential risks, the imaging of voids, faults, fluid areas, erratic boulders or other changes in material is essential. Exploratory drillings only provide an image of the geological parameters in the near-field of the borehole and lack in showing the detailed geological structure. Thus, acoustic analysis is a better choice as it offers the opportunity to obtain a detailed image of the soil with the help of seismic waves. Propagating through the ground, seismic waves are reflected, refracted, scattered and converted; resulting in a detailed fingerprint of the actual structure. Most of the techniques used nowadays for the detection of anomalies rely on travel time measurements and migration techniques, considering only compressional waves.

This paper proposes a novel perspective on learning, positing it as the pursuit of dynamical invariants -- data combinations that remain constant or exhibit minimal change over time as a system evolves. This concept is underpinned by both informational and physical principles, rooted in the inherent properties of these invariants. Firstly, their stability makes them ideal for memorization and integration into associative networks, forming the basis of our knowledge structures. Secondly, the predictability of these stable invariants makes them valuable sources of usable energy, quantifiable as kTln2 per bit of accurately predicted information. This energy can be harnessed to explore new transformations, rendering learning systems energetically autonomous and increasingly effective. Such systems are driven to continuously seek new data invariants as energy sources. The paper further explores several meta-architectures of autonomous, self-propelled learning agents that utilize predictable information patterns as a source of usable energy.

Leveraging recent advancements in large language models, modern neural code completion models have demonstrated the capability to generate highly accurate code suggestions. However, their massive size poses challenges in terms of computational costs and environmental impact, hindering their widespread adoption in practical scenarios. Dynamic inference emerges as a promising solution, as it allocates minimal computation during inference while maintaining the model's performance. In this research, we explore dynamic inference within the context of code completion. Initially, we conducted an empirical investigation on GPT-2, focusing on the inference capabilities of intermediate layers for code completion. We found that 54.4% of tokens can be accurately generated using just the first layer, signifying significant computational savings potential. Moreover, despite using all layers, the model still fails to predict 14.5% of tokens correctly, and the subsequent completions continued from them are rarely considered helpful, with only a 4.2% Acceptance Rate. These findings motivate our exploration of dynamic inference in code completion and inspire us to enhance it with a decision-making mechanism that stops the generation of incorrect code. We thus propose a novel dynamic inference method specifically tailored for code completion models. This method aims not only to produce correct predictions with largely reduced computation but also to prevent incorrect predictions proactively. Our extensive evaluation shows that it can averagely skip 1.7 layers out of 16 layers in the models, leading to an 11.2% speedup with only a marginal 1.1% reduction in ROUGE-L.

Real-time high-resolution wind predictions are beneficial for various applications including safe manned and unmanned aviation. Current weather models require too much compute and lack the necessary predictive capabilities as they are valid only at the scale of multiple kilometers and hours - much lower spatial and temporal resolutions than these applications require. Our work, for the first time, demonstrates the ability to predict low-altitude wind in real-time on limited-compute devices, from only sparse measurement data. We train a neural network, WindSeer, using only synthetic data from computational fluid dynamics simulations and show that it can successfully predict real wind fields over terrain with known topography from just a few noisy and spatially clustered wind measurements. WindSeer can generate accurate predictions at different resolutions and domain sizes on previously unseen topography without retraining. We demonstrate that the model successfully predicts historical wind data collected by weather stations and wind measured onboard drones.

Large Language Models (LLMs) have emerged as powerful tools for natural language processing tasks, revolutionizing the field with their ability to understand and generate human-like text. As the demand for more sophisticated LLMs continues to grow, there is a pressing need to address the computational challenges associated with their scale and complexity. This paper presents a comprehensive survey on hardware accelerators designed to enhance the performance and energy efficiency of Large Language Models. By examining a diverse range of accelerators, including GPUs, FPGAs, and custom-designed architectures, we explore the landscape of hardware solutions tailored to meet the unique computational demands of LLMs. The survey encompasses an in-depth analysis of architecture, performance metrics, and energy efficiency considerations, providing valuable insights for researchers, engineers, and decision-makers aiming to optimize the deployment of LLMs in real-world applications.

Material science literature is a rich source of factual information about various categories of entities (like materials and compositions) and various relations between these entities, such as conductivity, voltage, etc. Automatically extracting this information to generate a material science knowledge base is a challenging task. In this paper, we propose MatSciRE (Material Science Relation Extractor), a Pointer Network-based encoder-decoder framework, to jointly extract entities and relations from material science articles as a triplet ($entity1, relation, entity2$). Specifically, we target the battery materials and identify five relations to work on - conductivity, coulombic efficiency, capacity, voltage, and energy. Our proposed approach achieved a much better F1-score (0.771) than a previous attempt using ChemDataExtractor (0.716). The overall graphical framework of MatSciRE is shown in Fig 1. The material information is extracted from material science literature in the form of entity-relation triplets using MatSciRE.