A multivariate approach to determine electron beam parameters for a Monte Carlo 6 MV Linac model: Statistical and machine learning methods

Abstract Background Any Monte Carlo simulation of dose delivery using medical accelerator-generated megavolt photon beams begins by simulating electrons of the primary electron beam interacting with a target. Because the electron beam characteristics of any single accelerator are unique and generally unknown, an appropriate model of an electron beam must be assumed before MC simulations can be run. The purpose of the present study is to develop a flexible framework with suitable regression models for estimating parameters of the model of primary electron beam in simulators of medical linear accelerators using real reference dose profiles measured in a water phantom. Methods All simulations were run using PRIMO MC simulator. Two regression models for estimating the parameters of the simulated primary electron beam, both based on machine learning, were developed. The first model applies Principal Component Analysis to measured dose profiles in order to extract principal features of the shapes of the these profiles. The PCA-obtained features are then used by Support Vector Regressors to estimate the parameters of the model of the electron beam. The second model, based on deep learning, consists of a set of encoders processing measured dose profiles, followed by a sequence of fully connected layers acting together, which solve the regression problem of estimating values of the electron beam parameters directly from the measured dose profiles. Results of the regression are then used to reconstruct the dose profiles based on the PCA model. Agreement between the measured and reconstructed profiles can be further improved by an optimization procedure resulting in the final estimates of the parameters of the model of the primary electron beam. These final estimates are then used to determine dose profiles in MC simulations. Results Analysed were a set of actually measured (real) dose profiles of 6 MV beams from a real Varian 2300 C/D accelerator, a set of simulated training profiles, and a separate set of simulated testing profiles, both generated for a range of parameters of the primary electron beam of the Varian 2300 C/D PRIMO simulator. Application of the two-stage procedure based on regression followed by reconstruction-based minimization of the difference between measured (real) and reconstructed profiles resulted in achieving consistent estimates of electron beam parameters and in a very good agreement between the measured and simulated photon beam profiles. Conclusions The proposed framework is a readily applicable and customizable tool which may be applied in tuning virtual primary electron beams of Monte Carlo simulators of linear accelerators. The codes, training and test data, together with readout procedures, are freely available at the site: https://github.com/taborzbislaw/DeepBeam.

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Multi-Output Regression for Analyzing Power System Random States in Reliability Assessment by the Monte Carlo Method

Mathematics and Mathematical Modeling ◽

10.24108/mathm.0221.0000251 ◽

2021 ◽

pp. 49

Author(s):

D. A. Boyarkin

Keyword(s):

Machine Learning ◽

Monte Carlo ◽

Monte Carlo Method ◽

Power System ◽

Electric Power ◽

Reliability Assessment ◽

Electric Power System ◽

Learning Methods ◽

Machine Learning Methods ◽

The Monte Carlo Method

Increasing calculation speed of the electric power system (EPS) reliability of is one of the key issues in their operational management and long-term development planning. Analytical methods to assess the EPS reliability seem to be impossible due to large size of the problem and, as a consequence, essentially the only option for assessing is to use the Monte Carlo method. When it is used both the speed and the accuracy of calculation directly depend on the number of randomly generated system states and the complexity of their calculation in the model. Methods aimed at increasing computational efficiency can relate to two directions - reducing the states under consideration and simplifying the computational model for each state. Both options are performed provided that calculation accuracy is retained.The article presents research on using the machine learning methods and, in particular, the multi-output regression method to modernize the reliability assessment technique via the Monte Carlo method. Machine learning methods are used to determine the power deficit (realization of a random variable) for each random EPS state.The use of multi-output regression enables comprehensive determining of values of all the required variables. The experimental studies are based on the two test circuits of electric power systems: three-zone and IEEE RTS-96 with 24 zones of reliability.

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Monte Carlo Simulations of Au38(SCH3)24 Nanocluster Using Distance-Based Machine Learning Methods

The Journal of Physical Chemistry A ◽

10.1021/acs.jpca.0c01512 ◽

2020 ◽

Vol 124 (23) ◽

pp. 4827-4836 ◽

Cited By ~ 6

Author(s):

Antti Pihlajamäki ◽

Joonas Hämäläinen ◽

Joakim Linja ◽

Paavo Nieminen ◽

Sami Malola ◽

...

Keyword(s):

Machine Learning ◽

Monte Carlo ◽

Monte Carlo Simulations ◽

Learning Methods ◽

Machine Learning Methods

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PO-1352: Prediction of electron beam parameters of a Monte Carlo model using machine learning

Radiotherapy and Oncology ◽

10.1016/s0167-8140(21)01371-2 ◽

2020 ◽

Vol 152 ◽

pp. S716-S717

Author(s):

A. Wagner ◽

K. Brou Boni ◽

E. Rault ◽

F. Crop ◽

T. Lacornerie ◽

...

Keyword(s):

Machine Learning ◽

Monte Carlo ◽

Electron Beam ◽

Monte Carlo Model ◽

Beam Parameters

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DeepBeam – A Machine Learning Framework For Tuning The Primary Electron Beam of The PRIMO Monte Carlo Software

10.21203/rs.3.rs-425712/v1 ◽

2021 ◽

Author(s):

Zbisław Tabor ◽

Damian Kabat ◽

Michael Waligórski

Keyword(s):

Machine Learning ◽

Monte Carlo ◽

Electron Beam ◽

Regression Models ◽

Primary Electron ◽

Support Vector ◽

Linear Accelerators ◽

Primary Electron Beam ◽

Measured Dose ◽

Beam Parameters

Abstract BackgroundAny Monte Carlo simulation of dose delivery using medical accelerator-generated megavolt photon beams begins by simulating electrons of the primary electron beam interacting with a target. Because the electron beam characteristics of any single accelerator are unique and generally unknown, an appropriate model of an electron beam must be assumed before MC simulations can be run. The purpose of the present study is to develop a flexible framework with suitable regression models for estimating parameters of the model of primary electron beam in simulators of medical linear accelerators, basing on real reference dose profiles measured in a water phantom. MethodsAll simulations were run using PRIMO MC simulator. Two regression models for estimating the parameters of the simulated primary electron beam, both based on machine learning, were developed. The first model applies Principal Component Analysis to measured dose profiles in order to extract principal features of the shapes of the these profiles. The PCA-obtained features are then used by Support Vector Regressors to estimate the parameters of the model of the electron beam. The second model, based on deep learning, consists of a set of encoders processing measured dose profiles, followed by a sequence of fully connected layers acting together, which solve the regression problem of estimating values of the electron beam parameters directly from the measured dose profiles. Results of the regression are then used to reconstruct the dose profiles, basing on the PCA model. Agreement between the measured and reconstructed profiles can be further improved by an optimization procedure resulting in the final estimates of the parameters of the model of the primary electron beam. These final estimates are then used to determine dose profiles in MC simulations.ResultsAnalysed were a set of actually measured (real) dose profiles of 6 MV beams from a real Varian 2300 C/D accelerator, a set of simulated training profiles, and a separate set of simulated testing profiles, both generated for a range of parameters of the primary electron beam of the Varian 2300 C/D PRIMO simulator. Application of the two-stage procedure based on regression followed by reconstruction-based minimization of the difference between measured (real) and reconstructed profiles resulted in achieving consistent estimates of electron beam parameters and in a very good agreement between the measured and simulated photon beam profiles.ConclusionsThe proposed framework is a readily applicable and customizable tool which may be applied in tuning virtual primary electron beams of Monte Carlo simulators of linear accelerators. The codes, training and test data, together with some trained models and readout procedures, are freely available at the site: https://github.com/taborzbislaw/DeepBeam.

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Advanced surrogate modeling and machine learning methods in computational stochastic mechanics

10.12681/eadd/47178 ◽

2020 ◽

Author(s):

Ιωάννης Καλογερής

Keyword(s):

Machine Learning ◽

Monte Carlo ◽

Surrogate Modeling ◽

Stochastic Mechanics ◽

Learning Methods ◽

Machine Learning Methods

Η ποσοτικοποίηση της αβεβαιότητας στις παραμέτρους ενός μηχανικού συστήματος και οι μέθοδοι για τον προσδιορισμό της επιρροής της στην απόκριση αυτού αποτελούν ένα ουσιώδες κομμάτι της ανάλυσης και του σχεδιασμού των κατασκευών. Τις τελευταίες δεκαετίες αναπτύχθηκε η μέθοδος των στοχαστικών πεπερασμένων στοιχείων (ΣΠΣ), η οποία έχει ως στόχο τη μελέτη συστημάτων στα οποία ενυπάρχουν αβεβαιότητες στις παραμέτρους του συστήματος (πχ. ιδιότητες υλικών), στις συνοριακές συνθήκες, στη γεωμετρία και στη φόρτιση. Η κυριότερη και πιο διαδεδομένη μέθοδος στην κατηγορία των ΣΠΣ είναι η μέθοδος προσομοίωσης Monte Carlo. Στην πραγματικότητα, η μέθοδος αυτή είναι η μόνη ικανή να χειριστεί στοχαστικά προβλήματα στα οποία εμπλέκονται μη-γραμμικότητες, δυναμικές φορτίσεις, προβλήματα ευστάθειας, κλπ. Ωστόσο, για να επιτύχει υψηλή ακρίβεια απαιτεί ένα μεγάλο αριθμό τυχαίων προσομοιώσεων του υπολογιστικού μοντέλου για διάφορες τιμές των παραμέτρων. Ως συνέπεια, το υπολογιστικό κόστος αυτής της προσέγγισης καθίσταται ασύμφορο σε λεπτομερή μοντέλα με πολλούς βαθμούς ελευθερίας ή/και σε μη-γραμμικά δυναμικά προβλήματα, όπου η διάρκεια της μιας ανάλυσης κυμαίνεται από μερικά λεπτά έως μερικές ώρες. Με βάση αυτό το συμπέρασμα, η παρούσα ερευνητική προσπάθεια επικεντρώνεται στην εφαρμογή τεχνικών υποκατάστατης μοντελοποίησης και τεχνικών μηχανικής μάθησης με στόχο να παρακαμφθεί ο υπολογιστικός φόρτος της μεθόδου Monte Carlo. Στο πρώτο στάδιο της διατριβής, μελετάται η μέθοδος της εξέλιξης της πυκνότητας πιθανότητας ως μια εναλλακτική της Monte Carlo και προτείνονται κατάλληλες διατυπώσεις για την εφαρμογή της σε στατικά προβλήματα και σε μη-γραμμικά προβλήματα. Παράλληλα, προτείνεται ένα ακριβέστερο και αποδοτικότερο σχήμα πεπερασμένων στοιχείων βασισμένο στη μέθοδο Streamline Upwind/Petrov Galerkin για την επίλυση των μερικών διαφορικών εξισώσεων που προκύπτουν στα πλαίσια της μεθόδου. Εν συνεχεία, αναπτύσσεται το μαθηματικό και υπολογιστικό πλαίσιο για την εφαρμογή της μεθόδου των Φασματικών Στοχαστικών Πεπερασμένων στοιχείων σε στοχαστικά προβλήματα ραβδωτών φορέων με μη-γραμμικότητα γεωμετρίας. Τέλος, προτείνεται μια νέα μεθοδολογία κατασκευής υποκατάστατων μοντέλων βασισμένη στον αλγόριθμο των Χαρτών διάχυσης, ο οποίος ανήκει στην κατηγορία των μεθόδων μάθησης σε πολλαπλότητες. Με την προτεινόμενη μεθοδολογία το πλήρες προσομοίωμα των πεπερασμένων στοιχείων αντικαθίσταται από απλούστερες μαθηματικές σχέσεις με ελάχιστο κόστος υπολογισμού, επιτυγχάνοντας έτσι σημαντική μείωση του κόστους της μεθόδου Monte Carlo χωρίς ουσιαστικές απώλειες σε ακρίβεια.

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