Coordinate-Aware Modulation for Neural Fields

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.Comment: Project page: http://maincold2.github.io/cam

Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forward and inverse problems. While promising, the expensive computational costs to obtain solutions often restrict their broader applicability. We demonstrate that the computations in automatic differentiation (AD) can be significantly reduced by leveraging forward-mode AD when training PINN. However, a naive application of forward-mode AD to conventional PINNs results in higher computation, losing its practical benefit. Therefore, we propose a network architecture, called separable PINN (SPINN), which can facilitate forward-mode AD for more efficient computation. SPINN operates on a per-axis basis instead of point-wise processing in conventional PINNs, decreasing the number of network forward passes. Besides, while the computation and memory costs of standard PINNs grow exponentially along with the grid resolution, that of our model is remarkably less susceptible, mitigating the curse of dimensionality. We demonstrate the effectiveness of our model in various PDE systems by significantly reducing the training run-time while achieving comparable accuracy. Project page: https://jwcho5576.github.io/spinn/Comment: To appear in NeurIPS 2022 Workshop on The Symbiosis of Deep Learning and Differential Equations (DLDE) - II, 12 pages, 5 figures, full paper: arXiv:2306.1596

Separable Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate highly complex solution functions. The number of training points (collocation points) required on these challenging PDEs grows substantially, but it is severely limited due to the expensive computational costs and heavy memory overhead. To overcome this issue, we propose a network architecture and training algorithm for PINNs. The proposed method, separable PINN (SPINN), operates on a per-axis basis to significantly reduce the number of network propagations in multi-dimensional PDEs unlike point-wise processing in conventional PINNs. We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points (>10^7) on a single commodity GPU. The experimental results show drastically reduced computational costs (62x in wall-clock time, 1,394x in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy. Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation significantly faster than the best-performing prior method (9 minutes vs 10 hours in a single GPU), maintaining accuracy. Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation.Comment: arXiv admin note: text overlap with arXiv:2211.0876

Signal to noise ratio of upgraded imaging bolometer for KSTAR

An InfraRed imaging Video Bolometer (IRVB) was installed on KSTAR in 2012 having a ∼2 μm × 7 cm × 9 cm Pt foil blackened with graphite and a 5 mm × 5 mm aperture located 7.65 cm from the foil with 16 × 12 channels and a time resolution of 10 ms. The IR camera was an Indigo Phoenix (InSb, 320 × 256 pixels, 435 fps, <25 mK). In 2017, the IRVB was upgraded by replacing the IR camera with a FLIR SC7600 (InSb, 640 × 512 pixels, 105 fps, <25 mK). The aperture area was reduced by approximately half to 3.5 mm × 3.5 mm, and the number of channels was quadrupled to 32 × 24. A synthetic image derived using the projection matrix for the upgraded IRVB from a Scrape Off Layer Plasma Simulator (SOLPS) model with 146 kW of total radiated power had a maximum signal of 7.6 W/m2 and a signal to noise ratio (SNR) of 11. Experimental data for a plasma with parameters similar to the SOLPS model (total radiated power of 158 kW) had a maximum signal of 12.6 W/m2 and noise equivalent power density (SNR) of 0.9 W/m2 (14)

Reproduction of Gastric Cancer Prognostic Score by real-time quantitative polymerase chain reaction assay in an independent cohort

Purpose Addition of molecular markers to the American Joint Committee on Cancer (AJCC) staging system would allow further refinements in predicting recurrence and help individualize treatment decisions. We aimed to validate the Gastric Cancer Prognostic Score (GCPS) in an independent cohort using an easy and cost effective quantitative real-time polymerase chain reaction (qRT-PCR) assay. Methods We performed qRT-PCR using 48 samples from our previous study and expanded to 128 independent patients. The GCPS was recalculated using Cox regression estimates and the performance of cutoff values for GCPS was reassessed. Results The qRT-PCR results showed a similar pattern to nanostring data by scale function data comparison. Using a new cutoff value, GCPS stratified 95 stage IB–III patients who received adjuvant chemotherapy into 74 high-risk patients and 21 low-risk patients with significantly different recurrence-free survival (P< 0.0001). The survival difference remained significant (P= 0.028) in 27 patients who did not receive adjuvant chemotherapy. Among stage I and II patients who were treated with surgery only, one AJCC stage IIA patient was defined as low-risk and showed long-term survival. Nine of 12 high-risk patients showed recurrence less than 67 months after operation. Conclusion We reproduced the GCPS with an easily applicable qRT-PCR assay and successfully predicted recurrence in patients with gastric cancer

Fault detection and identification method using observer-based residuals

Manufacturing machinery is becoming increasingly complicated, and machinery breakdowns not only reduce efficiency, but also pose safety hazards. Due to the needs for maintaining high reliability within facility operation, various methods for condition monitoring are suggested as the importance of maintenance has increased. Among the various prognostics and health management (PHM) techniques, this paper introduces a model-based fault detection and isolation (FDI) technique for the diagnosis of machine health conditions. The proposed approach identifies faults by extracting fault signal information such as the magnitude or shape of the fault based on a defined relationship between a fault signal and observer theory. To validate the proposed method, a numerical simulation is conducted to demonstrate its fault detection and identification capabilities in various situations. The proposed method and data-driven methods are then compared with regard to their fault diagnosis performance. (C) 2018 Elsevier Ltd. All rights reserved

Anomaly Detection in Time Series Data and its Application to Semiconductor Manufacturing

Anomaly detection is essential for the monitoring and improvement of product quality in manufacturing processes. In the case of semiconductor manufacturing, where large amounts of time series data from equipment sensors are rapidly accumulated, identifying anomalous signals within this data presents a significant challenge. The data in question is multivariate and of varying lengths, with an often highly imbalanced ratio of normal to abnormal signals. Given the nature of this data, traditional data-driven methods may not be appropriate for its analysis. This paper proposes a novel unsupervised anomaly detection model for the analysis of multivariate time series data. The model utilizes a unique recurrent neural network architecture and a special objective function to detect anomalies. Furthermore, a relevance analysis method is introduced to facilitate the interpretation and analysis of the detected anomalous signals. Our experimental results indicate that this deep anomaly detection model, which summarizes sensor data of different lengths into a low-dimensional latent space, enabling the easy visualization and distinction of anomalous signals, can be applied in real-world semiconductor manufacturing factories and used by on-site engineers for both analysis and execution purposes