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NETL and H2 Resources Pty Ltd. will collaborate under this CRADA project to evaluate and design a scaled-up microwave assisted coal gasification process on Australian low-rank coal. This project will include parametric studies on the top size of feed coal using continuous feed microwave capabilities at NETL.
This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.
We propose the average spectrum norm to study the minimum number of measurements required to approximate a multidimensional array (i.e., sample complexity) via low-rank tensor recovery. Our focus is on the tensor completion problem, where the aim is to estimate a multiway array using a subset of tensor entries corrupted by noise. Our average spectrum norm-based analysis provides near-optimal sample complexities, exhibiting dependence on the ambient dimensions and rank that do not suffer from exponential scaling as the order increases.
Attention-based transformers are ubiquitous in machine learning applications from natural language processing to computer vision. In high energy physics, one central application is to classify collimated particle showers in colliders based on the particle of origin, known as jet tagging. In this work, we study the interpretatbility and prospects for acceleration of Particle Transformer (ParT), a state-of-the-art model, leverages particle-level attention to improve jet-tagging performance. We analyzing ParT's attention maps and particle-pair correlations in the eta-phi plane, revealing intriguing features, such as a binary attention pattern that identifies critical substructure in jets. These insights enhance our understanding of the model's internal workings and learning process and hint at ways to improve its efficiency. Along these lines, we also explore low-rank attention, attention alternatives, and dynamic quantization to accelerate transformers for jet tagging. With quantization, we achieve a 50% reduction in model size and a 10% increase in inference speed without compromising accuracy. These combined efforts enhance both the performance and the interpretability of transformers in high-energy physics, opening avenues for more efficient and physics-driven model designs.
In this work, we investigate improving the runtime performance of key computational kernels in the Python Tensor Toolbox (pyttb), a package for analyzing tensor data across a wide variety of applications. Recent runtime performance improvements have been demonstrated using Rust, a compiled language, from Python via extension modules leveraging the Python C API—e.g., web applications, data parsing, data validation, etc. Using this same approach, we study the runtime performance of key tensor kernels of increasing complexity, from simple kernels involving sums of products over data accessed through single and nested loops to more advanced tensor multiplication kernels that are key in low-rank tensor decomposition and tensor regression algorithms. In numerical experiments involving synthetically generated tensor data of various sizes and these tensor kernels, we demonstrate consistent improvements in runtime performance when using Rust from Python over 1) using Python alone, 2) using Python and the Numba just-in-time Python compiler (for loop-based kernels), and 3) using the NumPy Python package for scientific computing (for pyttb kernels).
We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins—including those containing few to no samples—and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.
Connected and Autonomous Vehicles (CAVs) technology has the potential to transform the transportation system. Although these new technologies have many advantages, the implementation raises significant concerns regarding safety, security, and privacy. Anomalies in sensor data caused by errors or cyberattacks can cause severe accidents. To address the issue, this study proposed an innovative anomaly detection algorithm, namely the LSTM Autoencoder with Gaussian Mixture Model (LAGMM). This model supports anomalous CAV trajectory detection in the real-time leveraging communication capabilities of CAV sensors. The LSTM Autoencoder is applied to generate low-rank representations and reconstruct errors for each input data point, while the Gaussian Mixture Model (GMM) is employed for its strength in density estimation. The proposed model was jointly optimized for the LSTM Autoencoder and GMM simultaneously. The study utilizes realistic CAV data from a platooning experiment conducted for Cooperative Automated Research Mobility Applications (CARMAs). The experiment findings indicate that the proposed LAGMM approach enhances detection accuracy by 3% and precision by 6.4% compared to the existing state-of-the-art methods, suggesting a significant improvement in the field.
In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.
This paper describes an efficient reverse-mode differentiation algorithm for contraction operations of tensor networks that may have arbitrary and unconventional network topologies. The approach leverages the tensor contraction tree of Evenbly and Pfeifer (2014), which provides an instruction set for the contraction sequence of a network. We show that this tree can be efficiently leveraged for differentiation of a full tensor network contraction using a recursive scheme that exploits (1) the bilinear property of contraction and (2) the property that trees have single path from root to leaves. While differentiation of tensor-tensor contraction is already possible in most automatic differentiation packages, we show that exploiting these two additional properties in the specific context of contraction sequences can improve efficiency. Following a description of the algorithm and computational complexity analysis, we investigate its utility for gradient-based supervised learning for low-rank function recovery and for fitting real-world unstructured datasets. We demonstrate improved performance over alternating least-squares optimization approaches and the capability to handle heterogeneous and arbitrary tensor network formats. When compared to alternating minimization algorithms, we find that the gradient-based approach requires a smaller oversampling ratio (number of samples compared to number model parameters) for recovery. This increased efficiency extends to fitting unstructured data of varying dimensionality and when employing a variety of tensor network formats. Here, we show improved learning using the hierarchical Tucker method over the tensor-train in high-dimensional settings on a number of benchmark problems.
This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases. (authors)
We present a novel Bayesian learning approach to outdoor radio heatmap construction utilizing deep Gaussian process (GP). The proposed approach employs a two-layer hierarchy which consists of two cascaded Gaussian processes that are capable of modeling more complex input-output relations than standard single-layer Gaussian processes. Since deriving the exact model likelihood is challenging, a lower bound is optimized instead so that gradient descent-based methods can be performed to find out the optimal model parameters. Typically, inducing points are used in GPs to facilitate low-rank approximation of covariance (kernel) matrices for computation speedup. However, the inaccuracy induced by inducing points can accumulate when stacking multiple layers of GP which may hinder the performance of deep GP. Moreover, since inducing points need to be learned, having them at all layers of deep GP also incurs computational burden. To overcome the above challenges, in contrast to the canonical deep GP model, we use a modified architecture where a full standard GP resides in the first layer and inducing points are only introduced for the second layer. This modified architecture strikes a balance between model accuracy and training complexity. In the proposed model, the noise parameter of the first GP layer is also eliminated to improve the training efficiency as the noise parameter at the output of the second layer suffices to model the uncertainty in the output. The proposed approach is evaluated on real-world datasets, in the form of location-Received Signal Strength (RSS) pairs, collected from the Platform for Open Wireless Data-driven Experimental Research (POWDER) located at the campus of the University of Utah. Experiment results show that the proposed approach can achieve smaller prediction errors on various training and testing data configurations than DNN-based and GP-based methods.
Deploying geospatial foundation models on resource-constrained edge devices demands compact architectures that maintain high downstream performance. However, their large parameter counts and the accuracy loss often induced by compression limit practical adoption.In this work, we leverage manifold-constrained optimization framework DLRT to compress large vision transformer–based geospatial foundation models during transfer learning. By enforcing structured low-dimensional parameterizations aligned with downstream objectives, this approach achieves strong compression while preserving task-specific accuracy. We show that the method outperforms of-the-shelf low-rank methods as LoRA. Experiments on diverse geospatial benchmarks confirm substantial parameter reduction with minimal accuracy loss, enabling high-performing, on-device geospatial models.
In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.
In this paper, we demonstrate the synthesis of magnetite-based, encapsulated catalyst with a core-shell structure from coal fly ash, an industrial solid waste, and its application to industrially important high temperature water-gas shift reaction (HT-WGSR). The catalyst precursor was first synthesized through a leaching-precipitation-hydrothermal process, leading to the formation of a nanosheet-like hematite precursor consisting of Fe 3+ as primary element and minor cations including Al 3+ , Mg 2+ and other cations (e.g. Ca 2+ and Ti 4+ ). During the WGSR, the nanosheets broke into smaller particles with a core of magnetite with a diameter of ~20 nm, whereas the inherent impurity elements were activated and migrated to the outer surface forming a shell with a thickness of ~4 nm. Due to the protection of shell, the as-synthesized catalyst exhibited improved activity, thermal stability and long-term durability for HT-WGSR at 400 °C and 450 °C. Compared to the pure hematite, this catalyst exhibited much higher activity and stability, i.e., increased CO conversion and decreased deactivation rate constant, by a factor of four and three, respectively. Additionally, through a bottom-up reverse synthesis, we have confirmed that Al 3+ functioned as a textual promoter enhancing the interfacial area of the catalyst. On the other hand, the presence of minor impurity elements, in particular 2.58 wt% Mg 2+ and 0.18 wt% Ti 4+ , were found to increase the basicity, and promote the adsorption rate of CO, the redox of catalysts, and the alteration of the reaction mechanism from regenerative to associative with the formation of a strong intermediate formate. Finally, this study not only opens a new direction on the valorization of solid waste into high-value catalysts, promoting the sustainability of solid waste management, but also provides an alternative, cost-effective and scalable approach for the design and fine-tuning of encapsulated catalysts.
The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. Here, we introduce the stochastic finite volume method within the tensor-train framework to counteract this limitation. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing tensor-train techniques for hyperbolic systems and conservation laws involving shocks.
This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.
Gradient coding is a method for mitigating straggling servers in a centralized computing network that uses erasure-coding techniques to distributively carry out first-order optimization methods. Randomized numerical linear algebra uses randomization to develop improved algorithms for large-scale linear algebra computations. In this study, we propose a method for distributed optimization that combines gradient coding and randomized numerical linear algebra. The proposed method uses a randomized ℓ 2 -subspace embedding and a gradient coding technique to distribute blocks of data to the computational nodes of a centralized network, and at each iteration the central server only requires a small number of computations to obtain the steepest descent update. The novelty of our approach is that the data is replicated according to importance scores, called block leverage scores, in contrast to most gradient coding approaches that uniformly replicate the data blocks. Furthermore, we do not require a decoding step at each iteration, avoiding a bottleneck in previous gradient coding schemes. We show that our approach results in a valid ℓ 2 -subspace embedding, and that our resulting approximation converges to the optimal solution.
We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the tensor train incremental core expansion (TT-ICE) improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE*). Here, we provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE* achieves 57× higher compression and up to 95% reduction in computational time.