Poisson's equation plays an important role in modeling many physical systems. In electrostatic self-consistent low-temperature plasma (LTP) simulations, Poisson's equation is solved at each simulation time step, which can amount to a significant computational cost for the entire simulation. In this paper, we describe the development of a generic machine-learned Poisson solver specifically designed for the requirements of LTP simulations in complex 2D reactor geometries on structured Cartesian grids. Here, the reactor geometries can consist of inner electrodes and dielectric materials as often found in LTP simulations. The approach leverages a hybrid CNN-transformer network architecture in combination with a weighted multiterm loss function. We train the network using highly-randomized synthetic data to ensure the generalizability of the learned solver to unseen reactor geometries. The results demonstrate that the learned solver is able to produce quantitatively and qualitatively accurate solutions. Furthermore, it generalizes well on new reactor geometries such as reference geometries found in the literature. To increase the numerical accuracy of the solutions required in LTP simulations, we employ a conventional iterative solver to refine the raw predictions, especially to recover the high-frequency features not resolved by the initial prediction. With this, the proposed learned Poisson solver provides the required accuracy and is potentially faster than a pure GPU-based conventional iterative solver. This opens up new possibilities for developing a generic and high-performing learned Poisson solver for LTP systems in complex geometries.
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Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) $=9$, results in a reduction of numerical defects by $25.2\%$ and FID improvement of $25.4\%$ (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.
Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.
Parkinson's disease (PD) is a slowly progressive, debilitating neurodegenerative disease which causes motor symptoms including gait dysfunction. Motor fluctuations are alterations between periods with a positive response to levodopa therapy ("on") and periods marked by re-emergency of PD symptoms ("off") as the response to medication wears off. These fluctuations often affect gait speed and they increase in their disabling impact as PD progresses. To improve the effectiveness of current indoor localisation methods, a transformer-based approach utilising dual modalities which provide complementary views of movement, Received Signal Strength Indicator (RSSI) and accelerometer data from wearable devices, is proposed. A sub-objective aims to evaluate whether indoor localisation, including its in-home gait speed features (i.e. the time taken to walk between rooms), could be used to evaluate motor fluctuations by detecting whether the person with PD is taking levodopa medications or withholding them. To properly evaluate our proposed method, we use a free-living dataset where the movements and mobility are greatly varied and unstructured as expected in real-world conditions. 24 participants lived in pairs (consisting of one person with PD, one control) for five days in a smart home with various sensors. Our evaluation on the resulting dataset demonstrates that our proposed network outperforms other methods for indoor localisation. The sub-objective evaluation shows that precise room-level localisation predictions, transformed into in-home gait speed features, produce accurate predictions on whether the PD participant is taking or withholding their medications.
Headland maneuvering is a crucial aspect of unmanned field operations for autonomous agricultural vehicles (AAVs). While motion planning for headland turning in open fields has been extensively studied and integrated into commercial auto-guidance systems, the existing methods primarily address scenarios with ample headland space and thus may not work in more constrained headland geometries. Commercial orchards often contain narrow and irregularly shaped headlands, which may include static obstacles,rendering the task of planning a smooth and collision-free turning trajectory difficult. To address this challenge, we propose an optimization-based motion planning algorithm for headland turning under geometrical constraints imposed by field geometry and obstacles.
Vision transformers have achieved leading performance on various visual tasks yet still suffer from high computational complexity. The situation deteriorates in dense prediction tasks like semantic segmentation, as high-resolution inputs and outputs usually imply more tokens involved in computations. Directly removing the less attentive tokens has been discussed for the image classification task but can not be extended to semantic segmentation since a dense prediction is required for every patch. To this end, this work introduces a Dynamic Token Pruning (DToP) method based on the early exit of tokens for semantic segmentation. Motivated by the coarse-to-fine segmentation process by humans, we naturally split the widely adopted auxiliary-loss-based network architecture into several stages, where each auxiliary block grades every token's difficulty level. We can finalize the prediction of easy tokens in advance without completing the entire forward pass. Moreover, we keep $k$ highest confidence tokens for each semantic category to uphold the representative context information. Thus, computational complexity will change with the difficulty of the input, akin to the way humans do segmentation. Experiments suggest that the proposed DToP architecture reduces on average $20\% - 35\%$ of computational cost for current semantic segmentation methods based on plain vision transformers without accuracy degradation.
Complex scenario of ultrasound image, in which adjacent tissues (i.e., background) share similar intensity with and even contain richer texture patterns than lesion region (i.e., foreground), brings a unique challenge for accurate lesion segmentation. This work presents a decomposition-coupling network, called DC-Net, to deal with this challenge in a (foreground-background) saliency map disentanglement-fusion manner. The DC-Net consists of decomposition and coupling subnets, and the former preliminarily disentangles original image into foreground and background saliency maps, followed by the latter for accurate segmentation under the assistance of saliency prior fusion. The coupling subnet involves three aspects of fusion strategies, including: 1) regional feature aggregation (via differentiable context pooling operator in the encoder) to adaptively preserve local contextual details with the larger receptive field during dimension reduction; 2) relation-aware representation fusion (via cross-correlation fusion module in the decoder) to efficiently fuse low-level visual characteristics and high-level semantic features during resolution restoration; 3) dependency-aware prior incorporation (via coupler) to reinforce foreground-salient representation with the complementary information derived from background representation. Furthermore, a harmonic loss function is introduced to encourage the network to focus more attention on low-confidence and hard samples. The proposed method is evaluated on two ultrasound lesion segmentation tasks, which demonstrates the remarkable performance improvement over existing state-of-the-art methods.
The quantum thermal average plays a central role in describing the thermodynamic properties of a quantum system. From the computational perspective, the quantum thermal average can be computed by the path integral molecular dynamics (PIMD), but the knowledge on the quantitative convergence of such approximations is lacking. We propose an alternative computational framework named the continuous loop path integral molecular dynamics (CL-PIMD), which replaces the ring polymer beads by a continuous loop in the spirit of the Feynman--Kac formula. By truncating the number of normal modes to a finite integer $N\in\mathbb N$, we quantify the discrepancy of the statistical average of the truncated CL-PIMD from the true quantum thermal average, and prove that the truncated CL-PIMD has uniform-in-$N$ geometric ergodicity. These results show that the CL-PIMD provides an accurate approximation to the quantum thermal average, and serves as a mathematical justification of the PIMD methodology.
We present SEIF, a methodology that combines static analysis with symbolic execution to verify and explicate information flow paths in a hardware design. SEIF begins with a statically built model of the information flow through a design and uses guided symbolic execution to recognize and eliminate non-flows with high precision or to find corresponding paths through the design state for true flows. We evaluate SEIF on two open-source CPUs, an AES core, and the AKER access control module. SEIF can exhaustively explore 10-12 clock cycles deep in 4-6 seconds on average, and can automatically account for 86-90% of the paths in the statically built model. Additionally, SEIF can be used to find multiple violating paths for security properties, providing a new angle for security verification.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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