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1. Probability flow solution of the Fokker–Planck equation

   https://doi.org/10.1088/2632-2153/ace2aa  

   Boffi, Nicholas M. ; Vanden-Eijnden, Eric ( July 2023 , Machine Learning: Science and Technology)

   The method of choice for integrating the time-dependent Fokker–Planck equation (FPE) in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation (SDE). Here, we study an alternative scheme based on integrating an ordinary differential equation that describes the flow of probability. Acting as a transport map, this equation deterministically pushes samples from the initial density onto samples from the solution at any later time. Unlike integration of the stochastic dynamics, the method has the advantage of giving direct access to quantities that are challenging to estimate from trajectories alone, such as the probability current, the density itself, and its entropy. The probability flow equation depends on the gradient of the logarithm of the solution (its ‘score’), and so isa-prioriunknown. To resolve this dependence, we model the score with a deep neural network that is learned on-the-fly by propagating a set of samples according to the instantaneous probability current. We show theoretically that the proposed approach controls the Kullback–Leibler (KL) divergence from the learned solution to the target, while learning on external samples from the SDE does not control either direction of the KL divergence. Empirically, we consider several high-dimensional FPEs from the physics of interacting particle systems. We find that the method accurately matches analytical solutions when they are available as well as moments computed via Monte-Carlo when they are not. Moreover, the method offers compelling predictions for the global entropy production rate that out-perform those obtained from learning on stochastic trajectories, and can effectively capture non-equilibrium steady-state probability currents over long time intervals.

    

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2. Equation of State and Spin Crossover of (Al, Fe)‐Phase H

   https://doi.org/10.1029/2022JB026291  

   Strozewski, Benjamin ; Buchen, Johannes ; Sturhahn, Wolfgang ; Ishii, Takayuki ; Ohira, Itaru ; Chariton, Stella ; Lavina, Barbara ; Zhao, Jiyong ; Toellner, Thomas S. ; Jackson, Jennifer M. ( April 2023 , Journal of Geophysical Research: Solid Earth)

   The transport of hydrogen into Earth's deep interior may have an impact on lower mantle dynamics as well as on the seismic signature of subducted material. Due to the stability of the hydrous phasesδ‐AlOOH (delta phase), MgSiO₂(OH)₂(phase H), andε‐FeOOH at high temperatures and pressures, their solid solutions may transport significant amounts of hydrogen as deep as the core‐mantle boundary. We have constrained the equation of state, including the effects of a spin crossover in the Fe³⁺atoms, of (Al, Fe)‐phase H: Al_0.84Fe³⁺_0.07Mg_0.02Si_0.06OOH, using powder X‐ray diffraction measurements to 125 GPa, supported by synchrotron Mössbauer spectroscopy measurements on (Al, Fe)‐phase H andδ‐(Al, Fe)OOH. The changes in spin state of Fe³⁺in (Al, Fe)‐phase H results in a significant decrease in bulk sound velocity and occurs over a different pressure range (48–62 GPa) compared withδ‐(Al, Fe)OOH (32–40 GPa). Changes in axial compressibilities indicate a decrease in the compressibility of hydrogen bonds in (Al, Fe)‐phase H near 30 GPa, which may be associated with hydrogen bond symmetrization. The formation of (Al, Fe)‐phase H in subducted oceanic crust may contribute to scattering of seismic waves in the mid‐lower mantle (∼1,100–1,550 km). Accumulation of 1–4 wt.% (Al, Fe)‐phase H could reproduce some of the seismic signatures of large, low seismic‐velocity provinces. Our results suggest that changes in the electronic structure of phases in the (δ‐AlOOH)‐(MgSiO₂(OH)₂)‐(ε‐FeOOH) solid solution are sensitive to composition and that the presence of these phases in subducted oceanic crust could be seismically detectable throughout the lower mantle.

    

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3. Historical Interstation Pattern Referencing (HIPR): An Application to PcP Waves Recorded in the Antarctic for ULVZ Imaging

   https://doi.org/10.1029/2021JB022741  

   Hansen, Samantha E. ; Garnero, Edward J. ; Rost, Sebastian ( October 2021 , Journal of Geophysical Research: Solid Earth)

   Much of our knowledge on deep Earth structure is based on detailed analyses of seismic waveforms that often have small amplitude arrivals on seismograms; therefore, stacking is essential to obtain reliable signals above the noise level. We present a new iterative stacking scheme that incorporates Historical Interstation Pattern Referencing (HIPR) to improve data quality assessment. HIPR involves comparing travel‐time and data quality measurements between every station for every recorded event to establish historical patterns, which are then compared to individual measurements. Weights are determined based on the individual interstation measurement differences and their similarity to historical averages, and these weights are then used in our stacking algorithm. This approach not only refines the stacks made from high‐quality data but also allows some lower‐quality events that may have been dismissed with more traditional stacking approaches to contribute to our study. Our HIPR‐based stacking routine is illustrated through an application to core‐reflected PcP phases recorded by the Transantarctic Mountains Northern Network to investigate ultra‐low velocity zones (ULVZs). We focus on ULVZ structure to the east of New Zealand because this region is well‐sampled by our data set and also coincides with the boundary of the Pacific Large Low Shear Velocity Province (LLSVP), thereby allowing us to further assess possible ULVZ‐LLSVP relationships. The HIPR‐refined stacks display strong ULVZ evidence, and associated synthetic modeling suggests that the ULVZs in this region are likely associated with compositionally distinct material that has perhaps been swept by mantle convection currents to accumulate along the LLSVP boundary.

    

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4. A Deep Learning-Based Real-time Seizure Detection System

   https://doi.org/10.1109/SPMB50085.2020.9353623  

   Shawki, N. ; Elseify, T. ; Cap, T. ; Shah, V. ; Obeid, I. ; Picone, J. ( December 2020 , Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium (SPMB))

   Obeid, Iyad Selesnick (Ed.)

   Electroencephalography (EEG) is a popular clinical monitoring tool used for diagnosing brain-related disorders such as epilepsy [1]. As monitoring EEGs in a critical-care setting is an expensive and tedious task, there is a great interest in developing real-time EEG monitoring tools to improve patient care quality and efficiency [2]. However, clinicians require automatic seizure detection tools that provide decisions with at least 75% sensitivity and less than 1 false alarm (FA) per 24 hours [3]. Some commercial tools recently claim to reach such performance levels, including the Olympic Brainz Monitor [4] and Persyst 14 [5]. In this abstract, we describe our efforts to transform a high-performance offline seizure detection system [3] into a low latency real-time or online seizure detection system. An overview of the system is shown in Figure 1. The main difference between an online versus offline system is that an online system should always be causal and has minimum latency which is often defined by domain experts. The offline system, shown in Figure 2, uses two phases of deep learning models with postprocessing [3]. The channel-based long short term memory (LSTM) model (Phase 1 or P1) processes linear frequency cepstral coefficients (LFCC) [6] features from each EEG channel separately. We use the hypotheses generated by the P1 model and create additional features that carry information about the detected events and their confidence. The P2 model uses these additional features and the LFCC features to learn the temporal and spatial aspects of the EEG signals using a hybrid convolutional neural network (CNN) and LSTM model. Finally, Phase 3 aggregates the results from both P1 and P2 before applying a final postprocessing step. The online system implements Phase 1 by taking advantage of the Linux piping mechanism, multithreading techniques, and multi-core processors. To convert Phase 1 into an online system, we divide the system into five major modules: signal preprocessor, feature extractor, event decoder, postprocessor, and visualizer. The system reads 0.1-second frames from each EEG channel and sends them to the feature extractor and the visualizer. The feature extractor generates LFCC features in real time from the streaming EEG signal. Next, the system computes seizure and background probabilities using a channel-based LSTM model and applies a postprocessor to aggregate the detected events across channels. The system then displays the EEG signal and the decisions simultaneously using a visualization module. The online system uses C++, Python, TensorFlow, and PyQtGraph in its implementation. The online system accepts streamed EEG data sampled at 250 Hz as input. The system begins processing the EEG signal by applying a TCP montage [8]. Depending on the type of the montage, the EEG signal can have either 22 or 20 channels. To enable the online operation, we send 0.1-second (25 samples) length frames from each channel of the streamed EEG signal to the feature extractor and the visualizer. Feature extraction is performed sequentially on each channel. The signal preprocessor writes the sample frames into two streams to facilitate these modules. In the first stream, the feature extractor receives the signals using stdin. In parallel, as a second stream, the visualizer shares a user-defined file with the signal preprocessor. This user-defined file holds raw signal information as a buffer for the visualizer. The signal preprocessor writes into the file while the visualizer reads from it. Reading and writing into the same file poses a challenge. The visualizer can start reading while the signal preprocessor is writing into it. To resolve this issue, we utilize a file locking mechanism in the signal preprocessor and visualizer. Each of the processes temporarily locks the file, performs its operation, releases the lock, and tries to obtain the lock after a waiting period. The file locking mechanism ensures that only one process can access the file by prohibiting other processes from reading or writing while one process is modifying the file [9]. The feature extractor uses circular buffers to save 0.3 seconds or 75 samples from each channel for extracting 0.2-second or 50-sample long center-aligned windows. The module generates 8 absolute LFCC features where the zeroth cepstral coefficient is replaced by a temporal domain energy term. For extracting the rest of the features, three pipelines are used. The differential energy feature is calculated in a 0.9-second absolute feature window with a frame size of 0.1 seconds. The difference between the maximum and minimum temporal energy terms is calculated in this range. Then, the first derivative or the delta features are calculated using another 0.9-second window. Finally, the second derivative or delta-delta features are calculated using a 0.3-second window [6]. The differential energy for the delta-delta features is not included. In total, we extract 26 features from the raw sample windows which add 1.1 seconds of delay to the system. We used the Temple University Hospital Seizure Database (TUSZ) v1.2.1 for developing the online system [10]. The statistics for this dataset are shown in Table 1. A channel-based LSTM model was trained using the features derived from the train set using the online feature extractor module. A window-based normalization technique was applied to those features. In the offline model, we scale features by normalizing using the maximum absolute value of a channel [11] before applying a sliding window approach. Since the online system has access to a limited amount of data, we normalize based on the observed window. The model uses the feature vectors with a frame size of 1 second and a window size of 7 seconds. We evaluated the model using the offline P1 postprocessor to determine the efficacy of the delayed features and the window-based normalization technique. As shown by the results of experiments 1 and 4 in Table 2, these changes give us a comparable performance to the offline model. The online event decoder module utilizes this trained model for computing probabilities for the seizure and background classes. These posteriors are then postprocessed to remove spurious detections. The online postprocessor receives and saves 8 seconds of class posteriors in a buffer for further processing. It applies multiple heuristic filters (e.g., probability threshold) to make an overall decision by combining events across the channels. These filters evaluate the average confidence, the duration of a seizure, and the channels where the seizures were observed. The postprocessor delivers the label and confidence to the visualizer. The visualizer starts to display the signal as soon as it gets access to the signal file, as shown in Figure 1 using the “Signal File” and “Visualizer” blocks. Once the visualizer receives the label and confidence for the latest epoch from the postprocessor, it overlays the decision and color codes that epoch. The visualizer uses red for seizure with the label SEIZ and green for the background class with the label BCKG. Once the streaming finishes, the system saves three files: a signal file in which the sample frames are saved in the order they were streamed, a time segmented event (TSE) file with the overall decisions and confidences, and a hypotheses (HYP) file that saves the label and confidence for each epoch. The user can plot the signal and decisions using the signal and HYP files with only the visualizer by enabling appropriate options. For comparing the performance of different stages of development, we used the test set of TUSZ v1.2.1 database. It contains 1015 EEG records of varying duration. The any-overlap performance [12] of the overall system shown in Figure 2 is 40.29% sensitivity with 5.77 FAs per 24 hours. For comparison, the previous state-of-the-art model developed on this database performed at 30.71% sensitivity with 6.77 FAs per 24 hours [3]. The individual performances of the deep learning phases are as follows: Phase 1’s (P1) performance is 39.46% sensitivity and 11.62 FAs per 24 hours, and Phase 2 detects seizures with 41.16% sensitivity and 11.69 FAs per 24 hours. We trained an LSTM model with the delayed features and the window-based normalization technique for developing the online system. Using the offline decoder and postprocessor, the model performed at 36.23% sensitivity with 9.52 FAs per 24 hours. The trained model was then evaluated with the online modules. The current performance of the overall online system is 45.80% sensitivity with 28.14 FAs per 24 hours. Table 2 summarizes the performances of these systems. The performance of the online system deviates from the offline P1 model because the online postprocessor fails to combine the events as the seizure probability fluctuates during an event. The modules in the online system add a total of 11.1 seconds of delay for processing each second of the data, as shown in Figure 3. In practice, we also count the time for loading the model and starting the visualizer block. When we consider these facts, the system consumes 15 seconds to display the first hypothesis. The system detects seizure onsets with an average latency of 15 seconds. Implementing an automatic seizure detection model in real time is not trivial. We used a variety of techniques such as the file locking mechanism, multithreading, circular buffers, real-time event decoding, and signal-decision plotting to realize the system. A video demonstrating the system is available at: https://www.isip.piconepress.com/projects/nsf_pfi_tt/resources/videos/realtime_eeg_analysis/v2.5.1/video_2.5.1.mp4. The final conference submission will include a more detailed analysis of the online performance of each module. ACKNOWLEDGMENTS Research reported in this publication was most recently supported by the National Science Foundation Partnership for Innovation award number IIP-1827565 and the Pennsylvania Commonwealth Universal Research Enhancement Program (PA CURE). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the official views of any of these organizations. REFERENCES [1] A. Craik, Y. He, and J. L. Contreras-Vidal, “Deep learning for electroencephalogram (EEG) classification tasks: a review,” J. Neural Eng., vol. 16, no. 3, p. 031001, 2019. https://doi.org/10.1088/1741-2552/ab0ab5. [2] A. C. Bridi, T. Q. Louro, and R. C. L. Da Silva, “Clinical Alarms in intensive care: implications of alarm fatigue for the safety of patients,” Rev. Lat. Am. Enfermagem, vol. 22, no. 6, p. 1034, 2014. https://doi.org/10.1590/0104-1169.3488.2513. [3] M. Golmohammadi, V. Shah, I. Obeid, and J. Picone, “Deep Learning Approaches for Automatic Seizure Detection from Scalp Electroencephalograms,” in Signal Processing in Medicine and Biology: Emerging Trends in Research and Applications, 1st ed., I. Obeid, I. Selesnick, and J. Picone, Eds. New York, New York, USA: Springer, 2020, pp. 233–274. https://doi.org/10.1007/978-3-030-36844-9_8. [4] “CFM Olympic Brainz Monitor.” [Online]. Available: https://newborncare.natus.com/products-services/newborn-care-products/newborn-brain-injury/cfm-olympic-brainz-monitor. [Accessed: 17-Jul-2020]. [5] M. L. Scheuer, S. B. Wilson, A. Antony, G. Ghearing, A. Urban, and A. I. Bagic, “Seizure Detection: Interreader Agreement and Detection Algorithm Assessments Using a Large Dataset,” J. Clin. Neurophysiol., 2020. https://doi.org/10.1097/WNP.0000000000000709. [6] A. Harati, M. Golmohammadi, S. Lopez, I. Obeid, and J. Picone, “Improved EEG Event Classification Using Differential Energy,” in Proceedings of the IEEE Signal Processing in Medicine and Biology Symposium, 2015, pp. 1–4. https://doi.org/10.1109/SPMB.2015.7405421. [7] V. Shah, C. Campbell, I. Obeid, and J. Picone, “Improved Spatio-Temporal Modeling in Automated Seizure Detection using Channel-Dependent Posteriors,” Neurocomputing, 2021. [8] W. Tatum, A. Husain, S. Benbadis, and P. Kaplan, Handbook of EEG Interpretation. New York City, New York, USA: Demos Medical Publishing, 2007. [9] D. P. Bovet and C. Marco, Understanding the Linux Kernel, 3rd ed. O’Reilly Media, Inc., 2005. https://www.oreilly.com/library/view/understanding-the-linux/0596005652/. [10] V. Shah et al., “The Temple University Hospital Seizure Detection Corpus,” Front. Neuroinform., vol. 12, pp. 1–6, 2018. https://doi.org/10.3389/fninf.2018.00083. [11] F. Pedregosa et al., “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res., vol. 12, pp. 2825–2830, 2011. https://dl.acm.org/doi/10.5555/1953048.2078195. [12] J. Gotman, D. Flanagan, J. Zhang, and B. Rosenblatt, “Automatic seizure detection in the newborn: Methods and initial evaluation,” Electroencephalogr. Clin. Neurophysiol., vol. 103, no. 3, pp. 356–362, 1997. https://doi.org/10.1016/S0013-4694(97)00003-9. 

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5. Deep learning closure models for large-eddy simulation of flows around bluff bodies

   https://doi.org/10.1017/jfm.2023.446  

   Sirignano, Justin ; MacArt, Jonathan F. ( July 2023 , Journal of Fluid Mechanics)

   Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$ . Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$ , especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications. 

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