Deep learning-based spatiotemporal multi-event reconstruction

Abstract

A method (800) of reconstructing particle detection events is provided. The method includes: obtaining signal data associated with a first particle detection event detected by a delay line detector (802); predicting a number of particles associated with the first particle detection event using a hit multiplicity classifier (806); if the number of particles associated with the first particle detection event is two or more, identifying a signal amplitude peak associated with each one of the two or more particles using a peak finding model (808); calculating, for each of the two or more particles, (i) a two-dimensional (2D) position with respect to delay lines of the delay line detector and (ii) a time-of-flight, based on the respective signal amplitude peak (810); and presenting an indication of the 2D position and the time-of-flight for each of the two or more particles (812). The method can be adapted to evaluate other signals with two or more closely spaced peaks.

Description

DEEP LEARNING-BASED SPATIOTEMPORAL MULTI-EVENT RECONSTRUCTIONSTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0001] This invention was made with government support under grant no. DE-SC0012447 awarded by the Department of Energy. The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims benefit of, and priority to, U.S. Provisional Application Serial No. 63 / 601,340, filed on November 21, 2023, and titled “DEEP LEARNING-BASED SPATIOTEMPORAL MULTI-EVENT RECONSTRUCTION.” The disclosure of which is hereby incorporated by reference in its entirety.BACKGROUND

[0003] The detection of single particles, such as atoms, ions, electrons, and highly energetic photons, is the cornerstone of many fields in fundamental physics research. However, it is often the case that the resulting signals (e.g., captured by a detector) due to a single particle is too faint to be measured directly and require amplification. Amplification is usually achieved with electron avalanches, as for example in photon multiplier tubes (PMTs) and microchannel plates (MCPs). MCPs offer the advantage that the incident particle can be spatially resolved with a phosphor screen or a wire-grid. The latter system is called a delay line detector (DLD); a spatially and temporally resolving detector that includes one or more layers of delay lines for detecting incident particles. DLDs can be used for ions, electrons, and photons with energies high enough to emit an electron from the front side of the MCP.

[0004] In ultra-fast atomic physics, DLDs can be used for cold target recoil ion momentum spectroscopy (COLTRIMS), a technique e.g., used for resolving the correlation of two simultaneously emitted electrons in non-sequential double ionization (NSDI). In other experiments, a DLD can be used to compare the bunching and anti-bunching behavior of free bosonic particles and free fermionic particles. Usually, the strength of correlation signals scales inversely with the separation of the particles, e.g., Coulomb interaction for electrons. Therefore, it is an important task to reconstruct particles that are as close as possible without errors. Despite the additional information provided by the multiple layers of delay lines, thedisentangling of two or more incident particle signals becomes increasingly more challenging the closer the particles get to each other. Although DLDs are effective in identifying and reconstructing single particle hits, they are much more limited in the ability to identify and reconstruct multi-hit events that are close in space and time. In such scenarios, the signals will significantly overlap and present reconstruction challenges.SUMMARY

[0005] In some aspects, the techniques described herein relate to a method of reconstructing particle detection events for a delay line detector, the method including: obtaining, by one or more processors, signal data from two or more signal channels of the delay line detector, the signal data associated with a first particle detection event detected by the delay line detector; predicting, by the one or more processors, a number of particles associated with the first particle detection event by evaluating the signal data using a hit multiplicity classifier, wherein the hit multiplicity classifier classifies the signal data into one of a plurality of classes each associated with a different number of particles; if the number of particles associated with the first particle detection event is two or more, identifying, by the one or more processors, a signal amplitude peak associated with each one of the two or more particles by evaluating the signal data using a peak finding model; calculating, by the one or more processors and for each of the two or more particles, (i) a two-dimensional (2D) position with respect to delay lines of the delay line detector and (ii) a time-of-flight, based on the respective signal amplitude peak; and presenting, by the one or more processors, an indication of the 2D position and the time-of-flight for each of the two or more particles.

[0006] In some aspects, the techniques described herein relate to a method, wherein obtaining the signal data includes: receiving analog signals from each of the two or more channels of the delay line detector; and converting the analog signals into digital signals using an analog-to-digital converter (ADC).

[0007] In some aspects, the techniques described herein relate to a method, further including preprocessing the digital signals by zero-padding.

[0008] In some aspects, the techniques described herein relate to a method, wherein the signal data is first signal data, the method further including: obtaining second signal data prior to obtaining the first signal data, wherein the second signal data is associated with a plurality of second particle detection events, wherein each of the plurality of second particle detection events is known to be associated with a single particle; and generating a training dataset of simulated multi -particle detection events by: identifying a peak signal amplitudeassociated with two or more events of the plurality of second particle detection events; shifting, in time, a position of the peak signal amplitude of at least one of the two or more events; and adding the peak signal amplitude of the two or more events.

[0009] In some aspects, the techniques described herein relate to a method, further including training the hit multiplicity classifier and the peak finding model using the training dataset.

[0010] In some aspects, the techniques described herein relate to a method, wherein the hit multiplicity classifier includes: one or more convolutional neural networks (CNN), wherein each of the one or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the one or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the one or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with the plurality of classes.

[0011] In some aspects, the techniques described herein relate to a method, wherein a class of the plurality of classes with a highest probability is selected as the predicted number of particles.

[0012] In some aspects, the techniques described herein relate to a method, wherein the peak finding model includes a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

[0013] In some aspects, the techniques described herein relate to a system including: at least one processor; and memory having instructions stored thereon that, when executed by the at least one processor, cause the system to: obtain signal data from two or more signal channels of a delay line detector, the signal data associated with a first particle detection event detected by the delay line detector; predict a number of particles associated with the first particle detection event by evaluating the signal data using a hit multiplicity classifier, wherein the hit multiplicity classifier classifies the signal data into one of a plurality of classes each associated with a different number of particles; if the number of particles associated with the first particle detection event is two or more, identify a signal amplitude peak associated with each one of the two or more particles by evaluating the signal data using a peak finding model; calculate, for each of the two or more particles, (i) a two-dimensional (2D) position with respect to delay lines of the delay line detector and (ii) a time-of-flight, based on the respective signal amplitude peak; and present an indication of the 2D position and the time-of-flight for each of the two or more particles.

[0014] In some aspects, the techniques described herein relate to a system, wherein obtaining the signal data includes to: receive analog signals from each of the two or more channels of the delay line detector; and convert the analog signals into digital signals using an analog-to-digital converter (ADC).

[0015] In some aspects, the techniques described herein relate to a system, wherein the instructions further cause the system to preprocess the digital signals by zero-padding.

[0016] In some aspects, the techniques described herein relate to a system, wherein the signal data is first signal data, and wherein the instructions further cause the system to: obtain second signal data prior to obtaining the first signal data, wherein the second signal data is associated with a plurality of second particle detection events, wherein each of the plurality of second particle detection events is known to be associated with a single particle; and generate a training dataset of simulated multi-particle detection events, including to: identify a peak signal amplitude associated with two or more events of the plurality of second particle detection events; shift, in time, a position of the peak signal amplitude of at least one of the two or more events; and add the peak signal amplitude of the two or more events.

[0017] In some aspects, the techniques described herein relate to a system, wherein the instructions further cause the system to train the hit multiplicity classifier and the peak finding model using the training dataset.

[0018] In some aspects, the techniques described herein relate to a system, wherein the hit multiplicity classifier includes: two or more convolutional neural networks (CNN), wherein each of the two or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the two or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the two or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with the plurality of classes.

[0019] In some aspects, the techniques described herein relate to a system, wherein a class of the plurality of classes with a highest probability is selected as the predicted number of particles.

[0020] In some aspects, the techniques described herein relate to a system, wherein the peak finding model includes a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

[0021] In some aspects, the techniques described herein relate to a method of reconstructing particle detection events for a delay line detector, the method including:obtaining, by one or more processors, first signal data from two or more signal channels of the delay line detector, the first signal data associated with a plurality of first particle detection events detected by the delay line detector, wherein each of the plurality of first particle detection events is known to be associated with a single particle; generating, by the one or more processors, a training dataset of simulated multi-particle detection events by: (i) identifying a peak signal amplitude associated with two or more events of the plurality of first particle detection events, (ii) shifting, in time, a position of the peak signal amplitude of at least one of the two or more events, and (iii) adding the peak signal amplitude of the two or more events; training, by the one or more processors, a hit multiplicity classifier and a peak finding model using the training dataset, wherein the hit multiplicity classifier is trained to predict a number of particles associated with a particle detection event detected by the delay line detector, and wherein the peak finding model is trained to identify signal amplitude peaks for each particle associated with a particle detection event; obtaining, by the one or more processors, second signal data from the two or more signal channels of the delay line detector, the second signal data associated with a second particle detection event detected by the delay line detector, the second particle detection event associated with an unknown number of particles; and reconstructing, by the one or more processors, the second particle detection event using the trained hit multiplicity classifier and the trained peak finding model.

[0022] In some aspects, the techniques described herein relate to a method, wherein reconstructing the second particle detection event includes: (i) determining a number of particles associated with the second particle detection event, and (ii) if the number of particles is two or more, identifying, for each particle, a two-dimensional (2D) position with respect to delay lines of the delay line detector and a time-of-flight.

[0023] In some aspects, the techniques described herein relate to a method, wherein the hit multiplicity classifier includes: two or more convolutional neural networks (CNN), wherein each of the two or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the two or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the two or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with a plurality of classes.

[0024] In some aspects, the techniques described herein relate to a method, wherein the peak finding model includes a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

[0025] Additional features will be set forth in part in the description which follows or may be learned by practice. The features will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive, as claimed.BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 is a diagram of an example delay line detector (DLD) setup, according to some implementations.

[0027] FIGS. 2 A and 2B are example time traces of a single-particle event and a doubleparticle event, respectively, according to some implementations.

[0028] FIG. 3 is a block diagram of an event reconstruction system, according to some implementations.

[0029] FIG. 4 is a diagram of a hit multiplicity classification model, according to some implementations.

[0030] FIG. 5 is a diagram of a peak finding model, according to some implementations.

[0031] FIGS. 6 A and 6B are graphs of example real and simulated single and doubleparticle events, according to some implementations.

[0032] FIG. 7A is a block diagram of an example event reconstruction or “inference” pipeline, according to some implementations.

[0033] FIG. 7B is a block diagram of an example simulation and training pipeline, according to some implementations.

[0034] FIG. 8 is a flow chart of a process for reconstructing a multi -particle event, according to some implementations.

[0035] FIG. 9 is a flow chart of a process for training a hit multiplicity classification model and a peak finding model, according to some implementations.

[0036] FIGS. 10A is a confusion matrix for a trained hit multiplicity classification model during testing, according to some implementations.

[0037] FIG. 10B is a chart of probabilities output by the hit multiplicity classification model during testing, according to some implementations.

[0038] FIGS. 11 A and 1 IB are graphs illustrating the performance of the peak finding model during testing, according to some implementations.

[0039] FIGS. 12A-12C are graphs of example hit events comparing the results of using the deep-learning based reconstruction techniques described herein and classical analysis techniques, according to some implementations.

[0040] FIGS. 13A and 13B are graphs illustrating the performance of the peak finding model during testing when including signals from the multichannel plate (MCP), according to some implementations.

[0041] FIG. 14 is a log plot of RMSE as a function of peak separation, according to some implementations.

[0042] FIGS. 15A and 15B are three-dimensional (3D) plots of RMSE as a function of peak separation and relative amplitude difference using a fit-based method and the peak finding model, respectively, according to some implementations.

[0043] FIG. 16 is an RMSE comparison between a fit-based method and the peak finding model, according to some implementations.

[0044] FIG. 17A is a diagram of an example experimental setup that includes a grid in front of the DLD, according to some implementations.

[0045] FIG. 17B-17E are position difference plots resulting from testing, according to some implementations.

[0046] Various objects, aspects, and features of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and / or structurally similar elements.DETAILED DESCRIPTION

[0047] Referring generally to the figures, a system and methods for spatiotemporal reconstruction of events are shown, according to various implementations. Specifically, the system and methods described herein can be used to reconstruct events in which two or more “peak” values (e.g., amplitude peaks) are present in a captured signal, where the two or more “peaks” are close enough in time or space that traditional reconstructions techniques are not able to differentiate the peaks. For example, event reconstruction is often performed in signal processing; yet many currently used event reconstruction techniques are not able to distinguish closely spaced events. As another example, the disclosed system and methods can be used to reconstruct particle hit events detected by a delay line detector (DLD). For brevity and clarity, the disclosed system and methods are generally described herein withrespect to DLD captured signals; however, it should be appreciated that the present disclosure is not intended to be limited only to use in DLD signal evaluation.

[0048] In implementation related to DLDs, the system and methods disclosed herein can be used to identify and reconstruct multi-particle events. A “multi-particle event,” as described herein, generally refers to an event where two or more particles that are close in time and / or space (e.g., due to being simultaneously or nearly-simultaneously emitted from a source) are detected by the DLD. As mentioned above, it can be particularly challenging to separate the signals from two or more such particles because the signals tend to overlap, particularly at the extremely short time scales considered for particle measurements. In this regard, the disclosed system and methods utilize machine learning techniques to identify and differentiate single and multi-hit events, and to reconstruct multi-hit events more effectively than other classic methods for analyzing DLD signal data. Notably, the machine-learning based approach described herein can substantially reduce the effective dead radius of simultaneously arriving particles, improving the overall quality of the reconstruction.

[0049] At a high-level, the machine-learning based event reconstruction approach described below utilizes a hit multiplicity classifier to determine a number of particles associated with a hit event and a peak finding model to identifying signal amplitude peaks in the DLD signal data associated with each identified particle. In this regard, the hit multiplicity classifier is a type of machine learning model configured to classify input data - in this case, DLD signal data - into one of a plurality of known classes. For example, the hit multiplicity classifier described herein can classify input DLD signal data for a particle detection event according to a predicted number of particles associated with particle detection event. For any particle detection events that are predicted as “multi-particle” events, the peak finding model can identify associated signal amplitude peaks which, in turn, can be used to calculate a position of each particle (e.g., an x and j’ position of each particle on the wireframe of the DLD, as discussed below) and a time-of-flight of the particle.Delay Line Detector Setup

[0050] Turning first to FIG. 1, a diagram of an example delay line detector (DLD) setup - referred to herein as experimental setup 100 - is shown, according to some implementations. Experimental setup 100 generally includes a DLD 102 that, itself, includes a delay line array 104 and a microchannel plate (MCP) 106. Delay line array 104 is shown as a biased meandering wireframe, having a number of wires each defining two signal channels (e.g., one channel associated with each end of a wire). In the specific configuration shown, delay line array 104 includes three wires configured to form six signal channels (e.g., shown as VI, V2,Ul, U2, Wl, and W2). In some implementations, MCP 106 is a Chevron type (double) microchannel plate detector. In some such implementations, the front of MCP 106 is a funnel-type MCP for high detection efficiency. Each of the signal channels associated with delay line array 104, as well as a signal channel associated with MCP 106, are coupled to an amplifier 108 which amplifies the received signals. Amplifier 108 is, in turn, coupled to an analog-to-digital converter (ADC) 110 to discretize the amplified signals. In some implementations, ADC 110 has a bin size of 0.8 ns. The digital signals can then be passed to a controller or a computer 112 for storage, further analysis, display, etc.

[0051] In the specific configuration shown, experimental setup 100 further includes a tungsten needle tip 114 that is illuminated with ultra-short few-cycle laser pulses 116, e.g., from an optical parametric amplifier system, causing electrons to be emitted from needle tip 114. In some implementations, needle tip 114 has an apex radius of 5 to 20 nm. In some implementations, laser pulses 116 have a central wavelength of 800 nm and a repetition rate of 200 kHz. In some implementations, the typical pulse duration is 12 fs. It should be noted, however, that each of these parameters is provided only as an example and is not intended to be limiting. As electron emission occurs promptly with the incident laser pulse, needle tip 114 and laser pulses 116 provide an ultra-fast electron source with initial pulse durations of a few femtoseconds that are far below any electronically resolvable time scale. Each electron that is incident to MCP 106 will cause a secondary electron emission, resulting in an electron bunch of 105— 106electrons. In some implementations, experimental setup 100 - or, at least, DLD 102 and needle tip 114 - are contained in an ultra-high vacuum chamber, e.g., having a base pressure smaller than 109mbar.

[0052] In operation, a negative bias voltage is applied to needle tip 114. In some implementations, the bias voltage is in the range of -15 to -50 V, corresponding to the final energy of the emitted electrons minus the influence of the laser field. Due to the negative bias, electrons are accelerated away from needle tip 114 and travel towards DLD 102. The electron bunch will induce a voltage pulse on MCP 106 at the same position where the incoming particle contacts or “hits” MCP 106. Likewise, the electron bunch will induce a voltage pulse in one or more wires of the delay line array 104. Specifically, two voltage pulses may be excited and travel in both directions in each wire of delay line array 104; thus, the voltage pulses can be detected at each end of the wire. As mentioned above, delay line array 104 includes three wireframes resulting in six channels where signals are recorded. Additionally, a seventh voltage signal can be picked up from the supply voltage of MCP 106, e.g., with the help of a bias tee.

[0053] Referring now to FIGS. 2A and 2B, example single-particle events and doubleparticle events are shown, according to some implementation. FIG. 2A, in particular, shows a time trace for a single-particle event, and FIG. 2B shows a time trace for a double-particle event. The “time traces” in each figure correspond to a measured voltage on each of the seven signal channels of experimental setup 100. It can be seen from FIGS. 2A and 2B that the voltage pulses measured in a single-particle event are smaller in amplitude than in the double-particle event. Additionally, two distinct “peaks” can be seen in each of Channels 1-6 in FIG. 2B (e.g., corresponding to a double-particle event).Event Reconstruction Using Deep Learning

[0054] Referring now to FIG. 3, a block diagram of an event reconstruction system 300 is shown, according to some implementations. As described herein, event reconstruction system 300 is generally configured to receive and process signal data from DLD 102 to reconstruction particle detection events. In this regard, “signal data,” as discussed above, generally includes analog or digital signals received from two or more channels of delay line array 104 (e.g., from at least one wire of delay line array 104, each wire defining two channels). Signal data generally corresponds to a voltage pulse induced on a wire of delay line array 104 responsive to a particle hit, as discussed in greater detail below.“Reconstructing” an event generally refers to determining a position on delay line array 104 where a particle is detected and a time that the particle contacted delay line array 104 (e.g., a time-of-flight). Event reconstruction system 300 addresses certain limitations of classical / existing reconstruction techniques when it comes to reconstruction multi-particle events, e.g., where two or more particles are closely positioned in time or space, as described in greater detail below.

[0055] However, as mentioned above, it should be appreciated that event reconstruction system 300 can also be adapted to reconstructing other types of events (e.g., outside of DLD implementations) where a signal may contain two or more closely spaced peaks. For example, in digital signal processing, a signal may contain two closely spaced but individual amplitude peaks. Therefore, “reconstructing” an event can more broadly refer to determine a position of two or more peaks in a signal, e.g., in time or with respect to a reference point. For the purposes of brevity and clarity, the following discussion focuses on implementations related to DLD signal evaluation.

[0056] Event reconstruction system 300 is shown to include a processing circuit 302 that includes a processor 304 and a memory 310. Processor 304 can be a general-purpose processor, an application specific integrated circuit (ASIC), one or more field programmablegate arrays (FPGAs), a group of processing components (e.g., a central processing unit (CPU), graphical processing unit (GPU), tensor processing unit (TPU), etc.), or other suitable electronic processing structures. In some implementations, processor 304 is configured to execute program code stored on memory 310 to cause event reconstruction system 300 to perform one or more operations, as described below in greater detail. It will be appreciated that, in implementations where event reconstruction system 300 is part of another computing device, the components of event reconstruction system 300 may be shared with, or the same as, the host device. For example, event reconstruction system 300 is implemented via computer 112, then event reconstruction system 300 may utilize the processing circuit, processor(s), and / or memory of computer 112 to perform the functions described herein; however, it should be understood that event reconstruction system 300 may replace computer 112, e.g., in experimental setup 100, in some implementations.

[0057] Memory 310 can include one or more devices (e.g., memory units, memory devices, storage devices, etc.) for storing data and / or computer code for completing and / or facilitating the various processes described in the present disclosure. In some implementations, memory 310 includes tangible (e.g., non-transitory), computer-readable media that stores code or instructions executable by processor 304. Tangible, computer-readable media refers to any physical media that is capable of providing data that causes event reconstruction system 300 to operate in a particular fashion. Example tangible, computer-readable media may include, but is not limited to, volatile media, non-volatile media, removable media and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Accordingly, memory 310 can include random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), electronically erasable programmable read-only memory (EEPROM), hard drive storage, temporary storage, non-volatile memory, flash memory, optical memory, or any other suitable memory for storing software objects and / or computer instructions. Memory 310 can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. Memory 310 can be communicably connected to processor 304, such as via processing circuit 302, and can include computer code for executing (e.g., by processor 304) one or more processes described herein.

[0058] While shown as individual components, it will be appreciated that processor 304 and / or memory 310 can be implemented using a variety of different types and quantities ofprocessors and memory. For example, processor 304 may represent a single processing device or multiple processing devices. Similarly, memory 310 may represent a single memory device or multiple memory devices. Additionally, in some implementations, event reconstruction system 300 may be implemented within a single computing device (e.g., one server, one housing, etc.). In other implementations, event reconstruction system 300 may be distributed across multiple servers or computers (e.g., that can exist in distributed locations). For example, event reconstruction system 300 may include multiple distributed computing devices (e.g., multiple processors and / or memory devices) in communication with each other that collaborate to perform operations. For example, but not by way of limitation, an application may be partitioned in such a way as to permit concurrent and / or parallel processing of the instructions of the application. Alternatively, the data processed by the application may be partitioned in such a way as to permit concurrent and / or parallel processing of different portions of a data set by the two or more computers.

[0059] Event reconstruction system 300 is also shown to include a communications interface 322 that facilitates communications between event reconstruction system 300 and any external components or devices, including as a remote device 330 (described in greater detail below) and / or DLD 102. In other words, communications interface 322 can transmit data to and / or receive data from DLD 102, remote device 330, or other external computing devices. Accordingly, communications interface 322 can be or can include a wired or wireless communications interface (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications, or a combination of wired and wireless communication interfaces. Communications via communications interface 322 can be direct (e.g., local wired or wireless communications) or via a network (e.g., a WAN, the Internet, a cellular network, etc.). For example, communications interface 322 may include one or more Ethernet ports for communicably coupling event reconstruction system 300 to a network (e.g., the Internet). In another example, communications interface 322 can include a Wi-Fi transceiver for communicating via a wireless communications network.

[0060] Memory 310 is shown to include a preprocessing engine 312 configured to (optionally) preprocess signal data received from DLD 102. Preprocessing can include any of a number of different techniques for cleaning, normalizing, or otherwise preparing the signal data. In some implementations, where event reconstruction system 300 receives analog (e.g., “raw”) signals from each channel of DLD 102, preprocessing engine 312 is configured to convert the analog signals into digital signals. In some such implementations, preprocessing engine 312 - or, more broadly, event reconstruction system 300 - can includean ADC. In other implementations, preprocessing engine 312 receives signal data in a digital format, having been converted by an extern ADC (e.g., ADC 110). In some implementations, preprocessing engine 312 performs zero-padding to ensure a constant vector length of received signal data. In some implementations, preprocessing engine 312 “cleans” the signal data by removing noise and artifacts, e.g., using one or more digital or analog filters.

[0061] After optional preprocessing - or, in cases where preprocessing is not separately performed, upon receiving signal data (e.g., in a digital format) - a hit multiplicity classifier 314 of memory 310 is configured to evaluate the signal data to distinguish among different hit multiplicity events. In other words, hit multiplicity classifier 314 is configured to evaluate the signal data to determine a number of particles associated with a particle detection event. In this regard, hit multiplicity classifier 314 is a type of classification model or “classifier” that is trained to predict a class for the input signal data. Each “class,” in the context of this disclosure, is associated with a different number of particles for a hit event. For example, hit multiplicity classifier 314 may consider four classes - one each for a single-particle event, a double-particle event, a triple-particle event, and a quadruple-particle event. However, it should be appreciated that hit multiplicity classifier 314 may be configured and / or trained to identify any number of classes (e.g., five or more particles).

[0062] As an input, hit multiplicity classifier 314 generally receives digitized signal data. In some implementations, signal data is evaluated offline. In other words, signals from each channel of DLD 102 are recorded, e.g., during an experiment, the signal data is evaluated after the experiment. In some such implementations, hit multiplicity classifier 314 can be configured to evaluate all of the signal data from an experiment. In other implementations, hit multiplicity classifier 314 can be configured to evaluate discrete portions of the signal data associated with hit events. For example, the captured signals can be evaluated (e.g., by preprocessing engine 312) to identify and isolate hit events and / or a segment of signal data may be captured responsive to detecting an event. As an output, hit multiplicity classifier 314 can provide a probability for each class, indicating a likelihood that the input data (e.g., the signal data) is associated with that class. In some implementations, hit multiplicity classifier 314 “predicts” the number of particles associated with a hit event by selecting a class with a highest probability.

[0063] Turning briefly to FIG. 4, an example implementation of hit multiplicity classifier 314 is shown in greater detail. As shown, hit multiplicity classifier 314 includes a plurality of convolution neural networks (CNNs) 402, with at least one CNN associated with each signal channel 404 received from DLD 102. In some implementations, each of CNNs 402 is a one-dimensional CNN that includes [ConvlD, BatchNorm, ReLu, ConvlD, BatchNorm, ReLu, GlobalAveragePooling] layers. The parameters of the model are optimized during training and the hyperparameters, num filters and kernel size, are optimized during hyperparameter optimization, as discussed in greater detail below. After flattening, the outputs of CNNs 402 are concatenated and passed through a dense neural network (DNN) 406. In some implementations, the DNN 406 includes [Dense, Dropout, Dense, Dropout] layers, where the number of neurons, dropout, and activation are hyperparameters. The last layer may have a number of neurons equivalent to the number of classes (e.g., four, in the example shown), with softmax activation outputs. It should be noted that, in some implementations, the input data to hit multiplicity classifier 314 (e.g., the signal data) is normalized prior to evaluation.

[0064] Referring again to FIG. 3, memory 310 is shown to further include a peak finder 316 configured to predict a position of signal amplitude peaks associated with multi-hit events. Specifically, peak finder 316 can be configured to evaluate signal data associated with a multi -particle event (e.g., as determined by hit multiplicity classifier 314) to identify a position of signal amplitude peaks associated with each particle. In this regard, peak finder 316 includes one or more peak finding models - one peak finding model associated with each of a different number of particles or “hits” - in some implementations. For example, peak finder 316 may include separately trained peak finding models for single-particle events, double-particle events, triple-particle events, quadruple-particle events, etc. For brevity, this disclosure generally considers a peak finding model configured for double-particle events; however, it should be appreciated that peak finder 316 is not intended to be limited in this regard. In some implementations, peak finder 316 can also include a separate peak finding model for evaluating signal data from 106, as discussed below. The output of peak finder 316, as also discussed in greater detail below, is a position in the signal of the signal amplitude peaks.

[0065] Turning briefly to FIG. 5, an example implementation of peak finder 316 is shown in greater detail. Specifically, FIG. 5 illustrates the architecture of the peak finding models utilized by peak finder 316, according to some implementations. As shown, input data (e.g., signal data or a segment of signal data) is provided as an input to a two-layer gated recurrent unit (GRU) 502. In some implementations, the signal amplitude is normalized for each channel ahead of time. A GRU is very similar to a long short-term memory (LSTM) network cell with a forget gate. In some implementations, GRU 502 is a bidirectional GRU to model steps through the time series in both directions. If the second GRU layer returns sequences, its output is flattened. Next, a set of [dropout, dense] layers 504 is used. A dense layerhaving two output neurons with sigmoid activation, one for each peak, produces the output of peak finder 316 (e.g., the peak positions). In some implementations, the sigmoid activation function is used because the peak positions are scaled to [0,1],

[0066] It should be appreciated that, while described herein as a two-layer GRU, the specific model utilized by peak finder 316 (e.g., in the architecture shown in FIG. 5) - e.g., GRU 502 - is not limited solely to GRUs. Rather, in certain other implementations, GRU 502 may be replaced by other types of recurrent layer models (e.g., LSTM), models including skip-connections, models with other normalization methods (e.g., group normalization or layer normalization), models including attention mechanism, a transformer, a graph neural network (GNN), or the like.

[0067] As mentioned above, MCP signals (e.g., signal data from MCP 106) tend to have a slightly different shape and a reduced signal width compared to the other channels of DLD 102. Therefore, peak finder 316 can include a separate peak finding model trained for MCP 106; however, the peak finding model for MCP data can have the same structure that is described above. In this regard, the peak finding model configured for MCP data can be trained using different training data. In some implementations, the model parameters are tuned during training on simulated MCP multi-particle events. The peak finding model hyperparameters may be optimized by training several models with different hyperparameters.

[0068] Referring yet again to FIG. 3, memory 310 is shown to further include a position calculator 318 configured to calculate a position and time - collectively referred to as spatiotemporal information - for each particle in a multi-particle event based on the output of peak finder 316 (e.g., the peak positions). Generally, position calculator 318 is configured to match the signal amplitude peaks and reconstruct the hit event. Position calculator 318 can output a position of each particle with respect to delay line array 104 (e.g., x and y position on delay line array 104 that the particle contacted) and a time that the particle was detected or contacted delay line array 104. In some implementations, position calculator 318 calculates the “position” of a particle hit (e.g., with respect to the lines of delay line array 104) from a velocity of the corresponding signals perpendicular to the lines of delay line array 104. Then, from the velocity and the time that the hit event occurred, a position can be calculated. For example, the position of a hit event, in one direction, can be calculated as the distance from the middle of the detector, x = 0.5vdt, where v is the velocity of the signal and dt is the difference between the peak times in associated channels (e.g., channels U1 and U2 when considering the U layer, as illustrated in FIG. 1).

[0069] In some implementations, “time” calculated by position calculator 318 refers to a time-of-flight of a particle; in other words, the time between when a particle emission is induced (e.g., by laser pulses 116 contacting needle tip 114) and a when the particle event is detected. For example, in some implementations, time-of-flight is calculated from the moment laser pulses 116 causes the emission of electrons from needle tip 114 to the moment that the electrons are detected by DLD 102. In some such implementations, the laser that generates laser pulses 116 can trigger a diode signal from which the time of flight of the electron can be calculated. Specifically, in some such implementations, the time-of-flight is calculated based on the diode signal and a peak in a signal recorded from MCP 106.

[0070] After reconstructing a hit event, position calculator 318 can be configured to store the calculated spatiotemporal information and / or can provide an indication of the spatiotemporal information, e.g., via a display or on a report. In some implementations, position calculator 318 can output the spatiotemporal information via a user interface, which can be presented on a display device (e.g., remote device 330) such as a screen. In some implementations, position calculator 318 can be configured to generate the user interface, which can include text, graphs, and other elements. In some such implementations, position calculator 318 may be configured to generate a user interface that provides a graphical representation (e.g., a diagram, picture, or graph) of the spatiotemporal information. For example, the user interface may include graphs or histograms of the position and / or time-of- flight associated with each particle.

[0071] Memory 310 is further shown to include a model trainer 320 configured to train hit multiplicity classifier 314 and / or the peaking finding models of peak finder 316.Specifically, model trainer 320 may use a training data set to tune (e.g., adjust) parameters of hit multiplicity classifier 314 and / or the peaking finding models. In this regard, model trainer 320 generally performs supervised or semi-supervised training. In some implementations, hyperparameter tuning is performed using a subset of a training dataset (or the full dataset) using a Keras Tuner and the Hyperband optimizer. Trained models with the best parameters and hyperparameters are retrained on the full training dataset. In some implementations, hit multiplicity classifier 314 is trained with categorical cross-entropy as the loss function.

[0072] In one specific implementation of hit multiplicity classifier 314, preferred hyperparameters were found to be: activation: ’relu’, dense l : 107, dense_2: 109, dropout: 0.3, kemel size l : 4, kemel_size_2: 10, leaming_rate: 0.001, num_filters: 27. For the peak finding models, other than for MCP data, mean square error (MSE) can be used as the loss function. In one specific implementation, preferred hyperparameters were found to be:GRU units: 10, activation: elu, clipnorm: 0.01, dropout: 0.3, hidden layer dim: 110, learning rate: 0.01, num layers: 1, ret seq: 1. For the peak finding model(s) configured to evaluate MCP data, preferred hyperparameters were found to be: GRU units: 45, activation: elu, clipnorm: 0.01, dropout: 0.2, hidden_layer_dim: 210, learning_rate: 0.01, num_layers: 1, ret seq: 0. It should be appreciated, however, that these hyperparameters are provided only for exemplary purposes and should not be considered limiting.

[0073] In some implementations, model trainer 320 is configured to generate the training dataset from single-particle events. In particular, since the voltage signals of single-particle events are approximately additive, it is possible to simulate multi-hit events through addition of single peak signals to obtain doubles, triples, quadruples, etc. An advantage of this approach is the exact knowledge of the individual peak positions without any shifts caused by a secondary hit. To get the single peaks needed for the simulated multi-hit events, model trainer 320 can use a fit-based classical peak finding algorithm (described below) to find the peaks in each signal channel and can then filter the peaks to keep only single-particle events. In some such implementations, model trainer 320 can use a filter (e.g., Savgol) to smooth a received signal and then search for maxima in the signal (e.g., a position where n positions to the left and right there are only lower values). If an event has more or less than one such maximum per channel, it is dropped. In other words, only events where exactly one peak was found in each channel are kept. Additionally, or alternatively, model trainer 320 may use an intermediate classification model or filtering based on the area under the obtained signal(s) to generate normalized signals. In some such implementations, a classifier may be trained to only identify single-hit events such that any events that cannot be “certainly” classified as a single-hit event (e.g., based on a threshold confidence score) are discarded. In some implementations, each channel is normalized by dividing every value through the max value in each channel and then the squares of the values of the signal are summed. In other implementations, the values or absolute values of the signal are summed. This can be repeated for all of the signal channels, the resulting values added, and then filtered events where the resulting value exceeds a threshold are filtered out (e.g., as these events will have broader signals and are most likely doubles).

[0074] To generate a simulated multi-hit event, two or more single-hit events are shifted in time (e.g., randomly) and added. For the purposes of this discussion, a double-particle event is considered in which two single-particle events are added. The peak positions in the generated multi-hit events are known to have the same accuracy as for the single-hit events. Since the peak finding model(s) discussed above predict peaks for each signal channelseparately, multi-hit events are simulated for each channel separately and then shuffled. As each signal channel has its own characteristics, with this approach, peak finder 316 sees a greater variety of double peak events.

[0075] With additional reference to FIGS. 6 A and 6B, two real and simulated double peaks are shown, demonstrating the additive properties of single particle events. In experimental data, single peaks were found to have a distribution that falls off at the end of the recorded time interval, resulting in a poor performance of peak finder 316 in these regions. In some implementations, this problem is addressed by randomly shifting the peaks such that the peak position of each peak is uniform in the given time interval. However, it should be appreciated that the present disclosure is not intended to be limiting in this regard; rather, in other implementations, a different distribution (e.g., uniform) of peaks may be used. The real and simulated double-particle events, shown in FIGS. 6A and 6B, look almost identical except at the edges of the signals that are far away from the center of the peaks. These parts of the signals are less relevant as they do not contain additional timing information of the peaks.

[0076] Remote device 330, as mentioned above, may include any device that can be communicably coupled to event reconstruction system 300. In some implementations, remote device 330 is another computer or another computing device, such as a server, a remote desktop, etc., to which event reconstruction system 300 can share information. For example, event reconstruction system 300 may transmit spatiotemporal information to remote device 330 after reconstructing a hit event. In some implementations, remote device 330 is or includes a display (e.g., an LED or LCD screen) for presenting user interfaces and / or other data. For example, remote device 330 can include a display for presenting spatiotemporal information as mentioned above.

[0077] Referring now to FIG. 7A, an event reconstruction or “inference” pipeline 700 for reconstructing multi-hit events using event reconstruction system 300 is shown, according to some implementation. Pipeline 700 generally outlines the machine learning based event reconstruction technique implemented by event reconstruction system 300; thus, pipeline 700 may be considered in conjunction with the description of event reconstruction system 300 above for a better understanding of the functionality of event reconstruction system 300 and the components thereof. As shown, pipeline 700 begins with obtaining signal data 702 associated with a particle detection event, which is provided to hit multiplicity classifier 314 for evaluation. Hit multiplicity classifier 314 outputs a prediction 704 of the number of particles associated with the particle detection event (e.g., a prediction of the whether theevent was a single-hit, a double-hit, a triple-hit, etc.). In this example, hit multiplicity classifier 314 outputs a prediction that the input signal data contains a double-particle event. Then, because the output of hit multiplicity classifier 314 indicates a double-hit event, peak finder 316 is used to identify a position of each signal amplitude peak 706 in the signal data (e.g., where a peak per channel is associated with one of each of the particles). In this example, the signal amplitude peaks are represented as “Peakl” and “Peak 2.” Finally, position calculator 318 calculates a position of the particles, with respect to the delay line array 104, and a time-of-flight of the particles - shown as spatiotemporal information 708 - based on the identified peaks.

[0078] Referring now to FIG. 8, a flow chart of a process 800 for reconstructing a multiparticle detection event is shown, according to some implementations. In some implementations, process 800 is implemented by event reconstruction system 300, as described above. In some respects, process 800 follows and builds on the descriptions of pipeline 700 provided above. It will be appreciated that certain steps of process 800 may be optional and, in some implementations, process 800 may be implemented using less than all of the steps. It will also be appreciated that the order of steps shown in FIG. 8 is not intended to be limiting.

[0079] At step 802, signal data associated with a particle detection event is obtained. As discussed above, the signal data may include signals from two or more channels of a DLD (e.g., DLD 102). In some such implementations, the signal data generally includes voltage measurements captured from the delay lines (e.g., delay line array 104) and / or an MCP (e.g., MCP 106) of the DLD. Notably, the signal data may be a segment of recorded signals from each of the two or more channels that is associated with a particle detection event (e.g., the detection of at least one particle “hitting” the DLD). For example, the signal data may be captured over a set time period where particle detection is expected to occur (e.g., during an experiment) and / or segments of recorded signals in which particle detection events are identified can be extracted.

[0080] At step 804, optionally, the signal data is preprocessed. As mentioned above, preprocessing can include any number of signal or data-processing techniques such as filtering and the like. In some implementations, preprocessing includes amplifying analog signals obtained from the two or more channels of the DLD and / or converting analog signals obtained from the two or more channels of the DLD into digital signals using an ADC. Alternatively, in some implementations, the DLD may include an ADC and thus may providethe signal data in digital format at step 802. In some implementations, preprocessing includes performing zero-padding to ensure a constant vector length of received signal data.

[0081] At step 806, a number of particles associated with the particle detection event is predicted using hit multiplicity classifier 314. As discussed above, hit multiplicity classifier 314 is generally a trained classification model that predicts a class for input data (e.g., the signal data) from a set of predefined classes. In this case, hit multiplicity classifier 314 is configured to predict a class that is associated with a number of particles (e.g., single, double, triple, etc.). In some implementations, hit multiplicity classifier 314 additionally, or alternatively, provides a probability for each class, the probabilities indicating a likelihood that the input data (e.g., the signal data) is associated with each class. In some implementations, hit multiplicity classifier 314 predicts the number of particles associated with a hit event by selecting a class with the highest probability or lowest error.

[0082] At step 808, a peak finding model is used to evaluate the signal data if it is determined (e.g., at step 806) that the signal data is associated with a multi-particle event. Specifically, the peak finding model (e.g., peak finder 316) is configured to identify a signal amplitude peak associated with each particle in the multi-particle event. In some implementations, the peak finding model is a single peak finding model that evaluates signal data from each channel of the DLD separately. In other implementations, the peak finding model refers to two or more peak finding models that are trained to separately evaluate different signal channels. For example, peak finder 316 can include a first peak finding model for evaluating signals from Channels 1-6 in DLD 102 and a second peak finding model for evaluating signals from MCP 106. In some implementations, differently trained peak finding models can also be used based on the number of particles predicted at step 806. For example, a first peak finding model may be used for double-particle events and a second peak finding model may be used for triple-particle events. In some such implementations, the peak finding models have a similar structure but are trained on different data.

[0083] At step 810, a position and time-of-flight for each particle in a multi -particle event is calculated based on the peak positions identified at step 808. Thus, the calculation of the position and time may be referred to as the “reconstruction” of the event. As described above, the position refers to a position of each particle with respect to delay line array 104 (e.g., x and position on delay line array 104 that the particle contacted). The time-of-flight of the particle can be calculated based on when that particle was detected by DLD 102 (e.g., contacted delay line array 104). In this regard, time-of-flight denotes the time between when the particle was detected (e.g., based on the position of the associated in peak in time) andwhen the particle was emitted by a source (e.g., needle tip 114, responsive to laser pulses 116).

[0084] At step 812, an indication of the spatiotemporal information (e.g., position and time- of-flight) can be presented, e.g., via a display or on a report. In some implementations, the spatiotemporal information is output via a user interface, which can be presented on a display device. In some implementations, the user interface includes text, graphs, and other elements. For example, the user interface can include a graphical representation (e.g., a diagram, picture, or graph) of the spatiotemporal information. For example, the user interface may include graphs of the position and / or time associated with each particle hit. In some implementations, the spatiotemporal information is used to generate a report, which is presented to a user.

[0085] For brevity, process 800 is generally described herein with respect to multi-particle events, e.g., detected by a DLD; however, as mentioned above, it should be understood that process 800 can also be applied to other signals that contain two or more closely spaced peaks. In some such implementations, at step 802, the signal data can include any signal that contains one or more peaks to be identified. Likewise, at step 806, a number of peaks in the signal data is determined using hit multiplicity classifier 314 (e.g., as opposed to predicting a number of “particles”). At step 808, an amplitude of each peak is identified using peak finder 316. Thus, process 800 can be adapted to identify two or more closely spaced peaks in a signal.Model Training

[0086] Referring now to FIG. 7B, a simulation and training pipeline 750 for hit multiplicity classifier 314 and / or the peaking finding models of peak finder 316 is shown, according to some implementations. Pipeline 750 begins with obtaining signal data associated with a plurality of particle detection events. In some implementations, each of the plurality of particle detection events are known to be associated with a single particle (e.g., “singleparticle events”); otherwise, the plurality of particle hit events may be filtered to identify a subset of the events that are determined to be associated with a single particle (e.g., at least with some level of confidence). The plurality of particle detection events that are associated with single particles are shown as singles 754.

[0087] As mentioned above, the two or more of the plurality of particle detection events can then be used to generate simulated multi-particle events 756 by shifting at least one of the two or more events and adding the two or more events together. In some implementations, the two or more single-particle events are randomly shifted in time before being added.Simulated multi- particle events 756 can then be used as a training dataset to train hit multiplicity classifier 314 and the peak finding models of peak finder 316. Specifically, as shown, hit multiplicity classifier 314 may be trained on all of the events - including both simulated multi-particle events 756 and the single-particle events used to generate simulated multi-particle events 756. In contrast, the peak finding models of peak finder 316 are trained only on the simulated multi-particle events 756, e.g., to identify peaks in double, triple, quadruple, etc., particle events.

[0088] Referring now to FIG. 9, a flow chart of a process 900 for training hit multiplicity classifier 314 and the peaking finding models of peak finder 316 is shown, according to some implementations. Accordingly, process 900 can be implemented by event reconstruction system 300 - or, more specifically, model trainer 320 - as described above. It will be appreciated that certain steps of process 900 may be optional and, in some implementations, process 900 may be implemented using less than all of the steps. It will also be appreciated that the order of steps shown in FIG. 9 is not intended to be limiting.

[0089] At step 902, signal data associated with a plurality of particle detection events is obtained. In some implementations, the signal data includes signals from two or more channels of a DLD (e.g., DLD 102) associated with a plurality of particle detection events. As described above, the signal data generally includes voltage measurements captured from the delay lines (e.g., delay line array 104) and / or an MCP (e.g., MCP 106) of the DLD. Notably, the signal data may be a segment of recorded signals from each of the two or more channels that is associated with a particle detection event. For example, the signal data may be captured over a set time period where a particle detection is expected to occur (e.g., during an experiment) and / or segments of recorded signals in which particle detection events are identified can be extracted.

[0090] At step 904, the signal data from the plurality of particle detection events are optionally filtered to include only single-particle events. For example, the signal data for each of the plurality of particle detection events may be evaluated manually or automatically (e.g., using a classifier) to identify single-particle events. In some implementations, an event is considered a “single-particle” event only if there is reasonable confidence in the classification. In some implementations, a fit-based classical peak finding algorithm (described below) or other classic algorithm is used to find the peaks in each signal channel; then, the signal data can be filtered to keep only single-particle events. In other implementations, the signal data obtained at 902 may be obtained from known single-particle events and thus does not require filtering.

[0091] At step 906, a training dataset of multi-particle events is generated from the obtained signal data. To generate a simulated multi-particle events, two or more singleparticle events - specifically, the signal amplitude peaks of the two or more single-particle events - are randomly shifted in time and added. This can be repeated any number of times to generate a training dataset of simulated multi -particle events. Alternatively, as mentioned above, two or more single-particle events may be combined without shifting in time.

[0092] At step 908, hit multiplicity classifier 314 is trained to determine a number of particles associated with a particle detection event based on the training data set and the originally obtained signal data associated with single-particle events. Training hit multiplicity classifier 314 can include adjusting parameters of hit multiplicity classifier 314 (e.g., the CNNs and DNN that make up hit multiplicity classifier 314) to minimize error. In this manner, hit multiplicity classifier 314 can be trained to predict which of a set of classes new signal data should be associated with.

[0093] At step 910, the peak finding model(s) of peak finder 316 are likewise trained to detect peaks in multi-particle events based on the training data set alone. As with training hit multiplicity classifier 314, training peak finder 316 can include adjusting parameters of peak finder 316 to minimize error. In addition, the hyperparameters may be optimized. After training and hyperparameter optimization, one or both the hit multiplicity classifier 314 and peak finder 316 can be used to evaluate subsequently obtained signal data as discussed above with respect to at least FIGS. 7 A and 8.

[0094] For brevity, process 900 is generally described herein with respect to multi-particle events, e.g., detected by a DLD; however, as mentioned above, it should be understood that process 900 can also be used to train hit multiplicity classifier 314 and peak finder 316 to evaluate other signals that contain two or more closely spaced peaks. In some such implementations, at step 902, the signal data can include any signal(s) that contain one or more peaks to be identified. In turn, at step 908, hit multiplicity classifier 314 is trained to determine a number of peaks in a signal (e.g., as opposed to being trained to determine a number of particles). At step 910, peak finder 316 is likewise trained to predict the position of peaks in a signal.Comparison to Other Event Reconstruction Techniques

[0095] Hardware-Based Time Stamp Detection: In many commercial DLDs, the determination of spatiotemporal (e.g., position (x, y) and time ( / )) information for the incoming particles relies on a hardware-based detection of the time stamps from the anodes and the MCP, combined with evaluation software. Generally, signals from the DLD are fedinto a CFD after amplification. The CFD superimposes an incoming signal with a copy that is electrically reversed and reduced by a factor of about three. Additionally, the original signal is shifted in time, which results in a well-defined zero crossing that defines the point in time where that specific signal arrived. To determine the zero crossing purely electrically, two comparators are used: one that provides a logic level of ‘ 1’ when a certain threshold is exceeded and another that provides a logic level of ‘ 1’ when the signal is above the zerovoltage level (e.g., noise-level). The time stamp is given by the point where both comparators provide / output a ‘ 1’ . The advantage of this method is that it is independent of the actual pulse height. The CFD outputs a nuclear instrument module (NIM) pulse with a well-defined shape, having a rising flank that is at the temporal position of the peak of the original signal. This NIM pulse is detected by a time-to-digital converter that digitizes the timing information with a resolution of approximately 25 ps.

[0096] Multi-Hit Capability of the Hardware-Based Time Stamps: While the time tags produced using the CFD method are robust, fast, and easy to handle, their multi-hit capability is limited when it comes to close-by events. For example, two equal peaks will result in only one zero-crossing if they are closer than about 1.9 times their full width at half maximum (FWHM). In absolute numbers, as the signals propagate with an average speed of 0.9 mm / ns, this leads to an average dead radius of 21 mm, as the FWHM of the norm-pulse is approximately 12.5 ns. Even before the dead radius is reached, problems such as shifts occur. If two particles hit the detector with a spatial distance smaller than the dead radius, only one particle will be reconstructed, and its position will be subject to error. The second particle can have even larger errors; yet it is known that the relative amplitude difference of the two peaks matters. If the distance between two particles is smaller than the dead radius, this shift is even more pronounced, and will result in one registered particle.

[0097] Analog Data Readout for Improved Classical Model Evaluation: F or applications that require better multi-hit capability compared to the basic hardware-based method, it is possible to utilize fast analog-to-digital converters (ADCs) to digitize each analog trace and use computer-based algorithms to obtain timing information. These “fast” ADCs can have a data rate of 300 MB / s, providing a theoretical measurement speed of about 400 kHz assuming an average data length of about 50 bins. After the data is recorded, offline data evaluation can be performed. The software of the ADCs can split multiple events on a single channel if they are separated long enough that the amplitude is lower than a preset trigger threshold. In this case all parts of each channel can be interpolated to the same time grid and then a peak finding algorithm can be used to search for the indices of peak maxima and toperform a fit on a window around them. However, even using this “fit-based” method, the error rate in reconstructing peaks is unacceptably high for closely spaced particles (e.g., having a separation of 10 ns or less).

[0098] Mean Pulse Curve Fit: Shifting and scaling single hit signals to the same position and height allows the extraction of a “mean pulse”. The double peak signal can then be fit to a sum of two mean pulses to reconstruct the two peaks. This method is referred to herein as “mean pulse curve fit” (MPCF). In order to be able to shift the mean pulse on a sub-bin level, the mean pulse is interpolated. The fit function then consists of a sum of two interpolated mean pulses, each shifted, scaled, and stretched. In a six-channel system, for example, there are six fit parameters, [xo, xi, ho, hi, so, sv], the peak positions xt, the peak heights hi, and the peak stretches st, where i E {0, 1}. Using a curve fit function, the six fit parameters are determined. The fit is initialized with random parameters. In some implementations, a fit is calculated for each channel individually (e.g., in a six channel system with MCP, that is a total of 42 parameters).

[0099] The quality of the fit depends upon the initial conditions; often, the outcome is visibly wrong. Several improvements are needed. First, bounds can be added to the fit parameters. For the positions xt, the bounds are the x-interval. Further, the peak heights ht to can be restricted, e.g., to \QA5hmax, 25hmax\, where hmaxis the maximal value of the given signal. Restricting the heights especially helps with close peak separations, because often a single mean pulse would fit quite well and the height of the second mean pulse would go to zero. The stretch is restricted to st = ±70%. Second, after performing the fit, the root mean square error (RMSE) is calculated and, if it is above some maximal value RMSEmax, the fit is performed again with new random initial parameters. The maximal RMSE is 3% of smaxand after 13 failed attempts it is multiplied with 1.15 every time a fit failed to be better than the current maximal RMSE.

[0100] A better way of initializing the fit parameters is to perform a fast peak finding algorithm on the signal. Since the fit often does not fulfill the RMSEmaxbound, and to conduct more attempts with slightly different initial conditions, the initial positions xt can be taken by sampling from a normal distribution with a variance c that increases with every attempted fit, starting with c = 20. The initial peak heights ht are sampled from a normal distribution with mean 0.75 hmaxand variance c = hmax15. The initial stretches st are also randomly sampled from a normal distribution around 1.0 with variance 0.3. After evaluation of the MPCF method on simulated double peak signals, it was found that the MPCF had a general bias in one direction. In testing, the peak positions of 10k simulated double-particlehit events were determined with the MPCF and the mean error calculated by comparison with the true peak positions. The bias was found to be -0.53, meaning yPred ~ ytrue was on average - 0.53.Testing and Results

[0101] Referring now to FIGS. 10A-17, in general, various results obtained through experimentation, e.g., testing using experimental setup 100 and event reconstruction system 300, are shown. In particular, event reconstruction system 300 was used to process the signals obtained from DLD 102, as discussed above. Below, certain results provided by event reconstruction system 300 are compared to the classical reconstruction techniques introduced above.

[0102] Looking first at FIGS. 10A and 10B, results of testing hit multiplicity classifier 314 are shown. Specifically, FIG. 10A shows a confusion matrix (true / predicted) for hit multiplicity classifier 314 tested with 106,544 evenly split test events. FIG. 10B shows probabilities for some random events. The most probable event class is underlined. All given events were predicted correctly. As can be seen from the confusion matrix, hit multiplicity classifier 314 is highly accurate, which results in the very high area under the curve (AUC) of greater than 0.9998 (one-vs-all).

[0103] Hit Multiplicity Classifier Results: Looking first at FIGS. 10A and 10B, results of testing Hit multiplicity classifier 314 are shown. Specifically, FIG. 10A shows a confusion matrix (true / predicted) for Hit multiplicity classifier 314 tested with test data set consisting of 106,544 events evenly split into single, double, triple, and quadruple-particle hit events. Hit multiplicity classifier 314 was found to have a test accuracy of 0.9951 for the test data set. FIG. 10B shows probabilities for some random events. The most probable event class is underlined. All given events were predicted correctly. As can be seen from the confusion matrix, hit multiplicity classifier 314 is highly accurate, with an area under the receiver operating characteristic (ROC) curve (AUC) greater than 0.9998 for every class (one-vs-all).

[0104] Deep Double Peak Finder Results (Channels 1 6): On the training data, the root mean square error (RMSE) of peak finder 316 was RMSEtratn = 1.03 ns and the mean average error (MAE) was MAEtrain = 0.25 ns. Evaluated on 1.2M simulated double-hit events, peak finder 316 was found to have an RMSE for the peak position RMSEtest = 1.72 ns and the MAE is MAEtest = 0.24. The bin size of the data was 0.8 ns.

[0105] FIGS. 11A and 1 IB illustrate the error distribution on 1.2M simulated doubleparticle hit event signals from all six channels of DLD 102 (e.g., not including the signal from MCP 106). Specifically, FIG. 11 A illustrates the RMSE distribution and FIG. 1 IBillustrates RMSE as a function of the peak distance. Overall, an error below 0.4 ns for peaks separated by more than 10 ns and an error below 0.9 ns for closer hits was observed. The mean error and variance tend to increase for smaller peak distances, demonstrating how closer peak positions are more difficult to determine.

[0106] FIGS. 12A-12C illustrate simulated double hit signals with their underlying single hit signals. Once the peaks get close enough, the position of the two underlying peaks will usually no longer coincide with the maxima of the curve. FIGS. 12A-12C specifically illustrate example events with simulated constructed double events. A solid line indicates the signal data that was used. FIG. 12A illustrates an event with two distinct peaks. The classical reconstruction techniques, as well as the machine learning based technique described herein, can capture both peaks well. FIG. 12B illustrates an event with two close peaks. In this case, the classical algorithms still identify two peaks, but they are reconstructed in at the wrong positions as both traces strongly overlap. FIG. 12C illustrates an event with two very closely located hits. Here, the disclosed machine learning based technique (e.g., implemented by event reconstruction system 300) is still able to find both peak positions, while the classical algorithms only finds one maximum which is not at any of the real peak positions.

[0107] Deep Double Peak Finder Results (MCP): Next, experimental setup 100 was tested on data from MCP 106. The test data consisted of 100k simulated MCP double peak signals. The root mean square error was RMSEtratn = 0.90 ns and RMSEtest = 0.83 ns. The mean average error was MAEtrain = 0.27 ns and MAEtest = 0.27 ns. The bin size of the data was 0.8 ns. As mentioned above, peak finder 316 uses a dropout layer during training but not during inference, which is why the training loss can be higher than the test loss. FIG. 13 A shows the RMSE distribution and FIG. 13B shows the RMSE as a function of peak distance. The performance of hit multiplicity classifier 314 and peak finder 316 when including signal data from MCP 106 is comparable to the performance illustrated in FIGS. 11 A and 1 IB.

[0108] FIG. 14 is a log plot of RMSE as a function of peak separation for Channels 1-6, not including an MCP signal. Specifically, FIG. 14 compares the disclosed machine learning based technique to the fit-based classical algorithm described above. The test data consisted of 3M generated signals from Channels 1-6 of DLD 102. The data was filtered such that no peaks are closer than 16 ns to one of the borders of the interval (e.g., since most methods do not work when a large part of the peak is cut off). For the error bars, a function was fit to the error distribution in each peak separation bin. The error bars correspond to one standard deviation of the fitted distribution.

[0109] As shown, the fit-based algorithm tends to perform well for distances greater than 30 ns. However, for peak distances smaller than around 22 ns (e.g., about the width of the peaks), the error of the fit-based algorithm significantly increases. In contrast, the performance of the disclosed machine learning based technique only slightly degrades. For much closer peaks, the classical algorithm appears to improve performance, since it is predicting only one peak once the two peaks have merged. If the peaks merge to one peak at exactly the same position, then the fit-based algorithm appears to give the correct result without knowing that there are two peaks. The same applies to the CFD method. The decrease in RMSE for peak separations closer than 10-20 ns for CFD and fit-based is purely this effect. If all the signals where only one peak is predicted are dropped, then this effect goes away.

[0110] A notable difference between RMSE and MAE in the classic peak finding models and peak finder 316 comes from a few large errors, as RMSE puts a higher weight on large errors. If all data points where the error is larger than 4 ns are removed (e.g., which amounts to 0.14% of the data), then RMSEtest = 0.60 ns and MAEtest = 0.21 ns. If position calculation software (e.g., position calculator 318) cannot reconstruct the event, it is typically discarded. A higher test loss than training loss indicates some amount of overfitting. Increasing dropout did not increase model performance on validation data. The performance of the models not only depends on the peak separation, but also on the amplitudes ao and ai of the underlying signals. Two peaks of about the same height can get closer to each other without merging to a single peak than two peaks with very different heights can.[OHl] In order to investigate the performance of the models with respect to the differences in amplitudes, a “relative amplitudes difference” metric, |a0— ai l / (ao +ai), is introduced. FIGS. 15A and 15B show 3D plots where the peak separation and the relative amplitudes difference are on the x-axis and -axis, and the z-axis contains the mean of the RMSE distribution for the respective bin. Now, a function of the peak separation and the relative amplitudes difference can be introduced, and the plots in FIGS. 15A and 15B reduced to two dimensions. This function is:motivated by the premise that it is hard to predict the peak positions when the peaks have a small separation and when the relative amplitudes difference is large. Thus, a region with small S, is hard to predict and a region with large S, is much easier to predict, as shown in FIG. 16. Constant S, corresponds to a straight line through the origin in the (rel. ampl. diff.)-(peakseparation) plane, and a point in FIG. 16 corresponds to the mean along the respective line. The error bars are from fitting a Rayleigh distribution to the RMSE distribution in the respective ^-bin and taking one standard deviation of the fitted distribution.

[0112] Real Data Inference: As a final check, the classical reconstruction methods are compared to the machine learning based reconstruction technique described herein using real data. To do so, a measurement was performed in which a copper grid (e.g., commercially available for sample preparation in transmission electron microscopy) is placed in front of the electron source as shown in FIG 17A. The shadow image of the grid is projected on the DLD (e.g., DLD 102); thus, there are sharp spatial features (e.g., in real space for the first and the second electron) but also for the difference plots in which Ay is plotted over Ax for the double hits. The clarity of the grid appearing in the reconstructed positions and difference plots is an indicator for the quality of the method’s performance.

[0113] FIG. 17B-17E include a number of 2D histograms illustrating the position differences of the x and j’ distances of the two particles. FIG. 17B shows the difference between two single hit events. This is an “ideal” plot obtained from two uncorrelated single hit events, showing a high resolution of the grid. There, no intrinsic dead radius or other double-hit based detector artifacts as well as possible physical correlations are present. FIG. 17C shows double hit events evaluated with the CFD-method. There is a star-shaped dead region with a maximal extension of about 30 mm where most events cannot be reconstructed. There are also other weaker six-fold artifacts. FIG. 17D shows double hit events evaluated with the fit-based classical peak finding algorithm. There are strong six-fold artifacts, too, and the dead radius is at about 20 mm. The strong hexagonal artifacts originate from the increasingly poorly determined peak positions as soon as the two signals come very close to each other. The associated signals of the individual electrons on the different layers cannot be clearly assigned by the evaluation software, which subsequently leads to these artifacts. FIG. 17E shows the same double events evaluated with peak finder 316. While some remaining six-fold artifacts are still visible, they are much weaker compared to the classical methods in FIG. 17C and FIG. 17D. At about 10 mm, the dead radius is much smaller and the grid appears much sharper in the region closer to the center.

[0114] The absolute numbers for the dead radius entirely depend on the FWHM of the pulse, here 12.5 ns (evaluated for a typical norm pulse). If the width of the norm pulse can be reduced by half through hardware changes, for example, then all dead radii can also be reduced by half, both those of the hardware-based evaluation and those of the classical algorithm as well as the machine-leaming-based evaluation. Typically, the particle speciescan influence the peak width, e.g., it should be smaller for ions. All given dead-radii are for true simultaneous hits, so two electrons arrive within a few ns or even below. If the arrival time of the particles is widely spread out, also the dead-radius will get smaller as the particles can get distinguished by the time-of-flight comparison.

[0115] As expected, the worst results were obtained using the hardware-based peak detection method with the CFD method. There is only one detectable zero crossing when two peaks come too close to each other. Therefore, a large dead radius is expected, and indeed observed in the difference plot in FIG. 17C. Additionally, the grid is barely visible in this plot. By comparison, FIG. 17B shows how the difference plot would look like for “ideally” resolved double hits, in which the grid in real space results in a nicely observable pattern in the difference plot.

[0116] Overall, the disclosed machine learning based reconstruction technique (e.g., implemented by hit multiplicity classifier 314 and peak finder 316, in part) performs better that the classical methods for peaks that are closer than 25-30 ns separation, down to and including 1 ns. How easily the peak positions can be determined not only depends on the peak separation, but also on the relative amplitudes of the two underlying peaks as illustrated in FIGS. 15A and 15B. The fit-based algorithm performs better for far peak separations for all values of the relative amplitude difference, whereas the disclosed machine learning based reconstruction technique results in a much smoother RMSE-mean-surface and stays lower and more consistent for closer peak separations. Combining peak separation and relative amplitude difference to a single variable FIG. 16 shows that for 2.7 < ^ < 72 [ns / mV], the disclosed machine learning based reconstruction technique outperforms the other methods. Again, for S, < 2.7 [ns] the fit-based method’s RMSE spuriously drops drastically, since here it (incorrectly) predicts one single peak.

[0117] Furthermore, based on the grid plots obtained with real data in FIGS. 17B-17E, it is clear that the disclosed machine learning based reconstruction technique performs better than the classical methods on real data, showing a much smaller dead radius, less artifacts and better resolution compared to classical methods. While this was to be expected from the comparison between real and simulated doubles in FIGS. 6A and 6B, the grid plots further confirm this conclusion.Configuration of Certain Implementations

[0118] The construction and arrangement of the systems and methods as shown in the various implementations are illustrative only. Although only a few implementations have been described in detail in this disclosure, many modifications are possible (e.g., variations insizes, dimensions, structures, shapes, and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative implementations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the implementations without departing from the scope of the present disclosure.

[0119] The present disclosure contemplates methods, systems, and program products on any machine-readable media for accomplishing various operations. Various implementations of the present disclosure may be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Implementations within the scope of the present disclosure include program products including machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine- readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machineexecutable instructions or data structures, and which can be accessed by a general purpose or special purpose computer or other machine with a processor.

[0120] When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general-purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions.

[0121] Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also, two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systemschosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.

[0122] It is to be understood that the methods and systems are not limited to specific synthetic methods, specific components, or to particular compositions. It is also to be understood that the terminology used herein is for the purpose of describing particular implementations only and is not intended to be limiting.

[0123] As used in the specification and the appended claims, the singular forms “a,” “an” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another implementation includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another implementation. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0124] “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur, and that the description includes instances where said event or circumstance occurs and instances where it does not.

[0125] Throughout the description and claims of this specification, the word “comprise” and variations of the word, such as “comprising” and “comprises,” means “including but not limited to,” and is not intended to exclude, for example, other additives, components, integers or steps. “Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal implementation. “Such as” is not used in a restrictive sense, but for explanatory purposes.

[0126] Disclosed are components that can be used to perform the disclosed methods and systems. These and other components are disclosed herein, and it is understood that when combinations, subsets, interactions, groups, etc. of these components are disclosed that while specific reference of each various individual and collective combinations and permutation of these may not be explicitly disclosed, each is specifically contemplated and described herein, for all methods and systems. This applies to all aspects of this application including, but not limited to, steps in disclosed methods. Thus, if there are a variety of additional steps that canbe performed it is understood that each of these additional steps can be performed with any specific implementation or combination of implementations of the disclosed methods.

Claims

WHAT IS CLAIMED IS:

1. A method of reconstructing particle detection events for a delay line detector, the method comprising: obtaining, by one or more processors, signal data from two or more signal channels of the delay line detector, the signal data associated with a first particle detection event detected by the delay line detector; predicting, by the one or more processors, a number of particles associated with the first particle detection event by evaluating the signal data using a hit multiplicity classifier, wherein the hit multiplicity classifier classifies the signal data into one of a plurality of classes each associated with a different number of particles; if the number of particles associated with the first particle detection event is two or more, identifying, by the one or more processors, a signal amplitude peak associated with each one of the two or more particles by evaluating the signal data using a peak finding model; calculating, by the one or more processors and for each of the two or more particles, (i) a two-dimensional (2D) position with respect to delay lines of the delay line detector and (ii) a time-of-flight, based on the respective signal amplitude peak; and presenting, by the one or more processors, an indication of the 2D position and the time- of-flight for each of the two or more particles.

2. The method of claim 1, wherein obtaining the signal data comprises: receiving analog signals from each of the two or more channels of the delay line detector; and converting the analog signals into digital signals using an analog-to-digital converter (ADC).

3. The method of claim 2, further comprising preprocessing the digital signals by zeropadding.

4. The method of claim 1, wherein the signal data is first signal data, the method further comprising:obtaining second signal data prior to obtaining the first signal data, wherein the second signal data is associated with a plurality of second particle detection events, wherein each of the plurality of second particle detection events is known to be associated with a single particle; and generating a training dataset of simulated multi-particle detection events by: identifying a peak signal amplitude associated with two or more events of the plurality of second particle detection events; shifting, in time, a position of the peak signal amplitude of at least one of the two or more events; and adding the peak signal amplitude of the two or more events.

5. The method of claim 4, further comprising training the hit multiplicity classifier and the peak finding model using the training dataset.

6. The method of claim 1, wherein the hit multiplicity classifier comprises: one or more convolutional neural networks (CNN), wherein each of the one or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the one or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the one or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with the plurality of classes.

7. The method of claim 6, wherein a class of the plurality of classes with a highest probability is selected as the predicted number of particles.

8. The method of claim 1, wherein the peak finding model comprises a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

9. A system comprising: at least one processor; and memory having instructions stored thereon that, when executed by the at least one processor, cause the system to:obtain signal data from two or more signal channels of a delay line detector, the signal data associated with a first particle detection event detected by the delay line detector; predict a number of particles associated with the first particle detection event by evaluating the signal data using a hit multiplicity classifier, wherein the hit multiplicity classifier classifies the signal data into one of a plurality of classes each associated with a different number of particles; if the number of particles associated with the first particle detection event is two or more, identify a signal amplitude peak associated with each one of the two or more particles by evaluating the signal data using a peak finding model; calculate, for each of the two or more particles, (i) a two-dimensional (2D) position with respect to delay lines of the delay line detector and (ii) a time-of-flight, based on the respective signal amplitude peak; and present an indication of the 2D position and the time-of-flight for each of the two or more particles.

10. The system of claim 9, wherein obtaining the signal data includes to: receive analog signals from each of the two or more channels of the delay line detector; and convert the analog signals into digital signals using an analog-to-digital converter (ADC).

11. The system of claim 10, wherein the instructions further cause the system to preprocess the digital signals by zero-padding.

12. The system of claim 9, wherein the signal data is first signal data, and wherein the instructions further cause the system to: obtain second signal data prior to obtaining the first signal data, wherein the second signal data is associated with a plurality of second particle detection events, wherein each of the plurality of second particle detection events is known to be associated with a single particle; and generate a training dataset of simulated multi-particle detection events, including to: identify a peak signal amplitude associated with two or more events of the plurality of second particle detection events;shift, in time, a position of the peak signal amplitude of at least one of the two or more events; and add the peak signal amplitude of the two or more events.

13. The system of claim 12, wherein the instructions further cause the system to train the hit multiplicity classifier and the peak finding model using the training dataset.

14. The system of claim 9, wherein the hit multiplicity classifier comprises: one or more convolutional neural networks (CNN), wherein each of the one or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the one or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the one or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with the plurality of classes.

15. The system of claim 14, wherein a class of the plurality of classes with a highest probability is selected as the predicted number of particles.

16. The system of claim 9, wherein the peak finding model comprises a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

17. A method of reconstructing particle detection events for a delay line detector, the method comprising: obtaining, by one or more processors, first signal data from two or more signal channels of the delay line detector, the first signal data associated with a plurality of first particle detection events detected by the delay line detector, wherein each of the plurality of first particle detection events is known to be associated with a single particle; generating, by the one or more processors, a training dataset of simulated multi-particle detection events by: (i) identifying a peak signal amplitude associated with two or more events of the plurality of first particle detection events, (ii) shifting, in time, a position of the peak signal amplitude of at least one of the two or more events, and (iii) adding the peak signal amplitude of the two or more events;training, by the one or more processors, a hit multiplicity classifier and a peak finding model using the training dataset, wherein the hit multiplicity classifier is trained to predict a number of particles associated with a particle detection event detected by the delay line detector, and wherein the peak finding model is trained to identify signal amplitude peaks for each particle associated with a particle detection event; obtaining, by the one or more processors, second signal data from the two or more signal channels of the delay line detector, the second signal data associated with a second particle detection event detected by the delay line detector, the second particle detection event associated with an unknown number of particles; and reconstructing, by the one or more processors, the second particle detection event using the trained hit multiplicity classifier and the trained peak finding model.

18. The method of claim 17, wherein reconstructing the second particle detection event includes: (i) determining a number of particles associated with the second particle detection event, and (ii) if the number of particles is two or more, identifying, for each particle, a two- dimensional (2D) position with respect to delay lines of the delay line detector and a time-of- flight.

19. The method of claim 17, wherein the hit multiplicity classifier comprises: one or more convolutional neural networks (CNN), wherein each of the one or more CNNs is associated with a signal channel of the two or more signal channels of the delay line detector such that each of the one or more CNNs separately receives data associated with one of the two or more signal channels; and a dense neural network (DNN), wherein an output of each of the one or more CNNs is concatenated and provided as an input to the DNN, and wherein the DNN outputs a probability associated with a plurality of classes.

20. The method of claim 17, wherein the peak finding model comprises a bi-directional gated recurrent unit (GRU), a dropout layer, and a dense layer.

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