[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128767-en":3,"doc-seo-128767-105":31,"detail-sidebar-cat-0-en-105":96},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128767,1099523882367,"Hazel","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",8,"Research & Report","A Machine Learning Approach for Predicting Particle Spatial, Velocity, and Temperature Distributions in Cold Spray Additive Manufacturing","Masked cold spray additive manufacturing (CSAM) is investigated for fabricating nickel-based electrodes with pyramidal pin-fins to enlarge the active area for the hydrogen-evolution reaction (HER). To avoid costly purely CFD-driven optimization, a two-stage machine learning framework is trained on 48 high-fidelity CFD simulations. Stage 1 uses sampling with K-nearest-neighbor kernel density estimation to predict particle spatial distributions and reallocate under-estimated regions. Stage 2 combines sampling, interpolation, symbolic regression, and a weighted random forest to predict particle velocity and temperature upon impact. Predictions closely match CFD outputs while reducing computation time by orders of magnitude, and the framework generalizes to unmasked configurations.","Article  \nA Machine Learning Approach for Predicting Particle Spatial, Velocity, and Temperature Distributions in Cold Spray Additive Manufacturing  \nLurui Wang , Mehdi Jadidi * and Ali Dolatabadi  \nAcademic Editor: Rocco Furferi  \nReceived: 26 April 2025  \nRevised: 1 June 2025  \nAccepted: 3 June 2025  \nPublished: 7 June 2025  \nCitation: Wang, L.; Jadidi, M.; Dolatabadi, A. A Machine Learning Approach for Predicting Particle Spatial, Velocity, and Temperature Distributions in Cold Spray Additive Manufacturing. Appl. Sci. 2025, 15, 6418. [https://doi.org/10.3390/](https://doi.org/10.3390/)[ ](https://doi.org/10.3390/)app15126418  \nCopyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://creativecommons.org/](https://creativecommons.org/)[ ](https://creativecommons.org/)[licenses/by/4.0/](licenses/by/4.0/)) .  \nDepartment of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Rd.,  \nToronto, ON M5S 3G8, Canada; [lurui.wang@mail.utoronto.ca](lurui.wang@mail.utoronto.ca) (L.W.); [ali.dolatabadi@utoronto.ca](ali.dolatabadi@utoronto.ca) (A.D.)  \n* [Correspondence: mehdi.jadidi@utoronto.ca](Correspondence: mehdi.jadidi@utoronto.ca)  \nAbstract: Masked cold spray additive manufacturing (CSAM) is investigated for fabricating nickel-based electrodes with pyramidal pin-fins that enlarge the active area for the hydrogen-evolution reaction (HER) . To bypass the high cost of purely CFD-driven optimization, we construct a two-stage machine learning (ML) framework trained on 48 high-fidelity CFD simulations. Stage 1 applies sampling and a K-nearest-neighbor kerneldensity-estimation algorithm that predicts the spatial distribution of impacting particles and re-allocates weights in regions of under-estimation. Stage 2 combines sampling, interpolation and symbolic regression to extract key features, then uses a weighted random forest model to forecast particle velocity and temperature upon impact. The ML predictions closely match CFD outputs while reducing computation time by orders of magnitude, demonstrating that ML-CFD integration can accelerate CSAM process design. Although developed for a masked setup, the framework generalizes readily to unmasked cold spray configurations.  \nKeywords: cold spray; additive manufacturing; machine learning; particle; velocity; temperature  \n1. Introduction  \nCold spray is an advanced additive manufacturing and repair process that utilizes high-pressure carrier gases, such as nitrogen or helium, to accelerate solid micron-sized particles to high velocities through a converging-diverging nozzle. This technique enables rapid material deposition without melting, relying solely on the particles’ kinetic energy for adhesion [1–5] . Upon impact with the substrate, the particles undergo severe plastic deformation, forming strong bonds with the surface. This low-temperature process avoids the thermal damage typically associated with high-temperature methods, preserving the original properties of both the feedstock and the substrate [3,6] . As a result, cold spray is particularly advantageous for industrial applications requiring high-quality, thermally sensitive material deposition.  \nIn high-pressure cold spray systems, operating pressures range from 1 to 5 MPa, with gas temperatures reaching up to 1100 ◦ C—remaining below the melting point of the particles [7] . Under these conditions, particles are accelerated to velocities typically between 500 and 1000 m/s. A crucial parameter in the deposition process is the standoff distance (SOD), which defines the gap between the nozzle exit and the substrate [2] . Along with SOD, factors such as nozzle geometry, operating conditions, particle type and size, and carrier gas properties play a significant role in determining particle velocity and  \ntemperature upon impact, deposition efficiency (DE)","cbCainoUZQgZG8WM","https://ap.wps.com/l/cbCainoUZQgZG8WM","pdf",9491378,2,1,43,"English","en",105,"# Introduction\n## Cold spray fundamentals\n## Process parameters affecting particle impact outcomes\n## Motivation from hydrogen evolution reaction (HER)\n## Masked electrode fabrication and surface modification","[{\"question\":\"为什么需要用机器学习来预测冷喷涂增材制造中的粒子分布？\",\"answer\":\"纯粹依赖 CFD 的优化成本很高。文中通过机器学习在少量高保真 CFD 数据上建立预测框架，以降低计算代价。\"},{\"question\":\"两阶段机器学习框架分别做什么预测任务？\",\"answer\":\"第一阶段用采样与 K 近邻核密度估计预测粒子空间分布，并对欠估区域重新分配权重；第二阶段用采样、插值、符号回归提取关键特征，再用加权随机森林预测粒子撞击时的速度与温度。\"},{\"question\":\"该方法在结果上与 CFD 如何对比？是否提升了效率？\",\"answer\":\"机器学习预测与 CFD 输出高度吻合，同时计算时间可降低到原来的量级，从而加速冷喷涂过程设计。\"},{\"question\":\"该框架是否只适用于掩模（masked）冷喷涂？\",\"answer\":\"虽然框架针对掩模设置开发，但文中指出其能够方便地推广到未掩模（unmasked）的冷喷涂配置。\"}]","A Machine Learning Approach for Predicting Particle Spatial, Velocity, and Temperature Distributions in Cold Spray Additive Manufacturing | 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CFD 的优化成本很高。文中通过机器学习在少量高保真 CFD 数据上建立预测框架，以降低计算代价。","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"两阶段机器学习框架分别做什么预测任务？",{"text":81,"@type":77},"第一阶段用采样与 K 近邻核密度估计预测粒子空间分布，并对欠估区域重新分配权重；第二阶段用采样、插值、符号回归提取关键特征，再用加权随机森林预测粒子撞击时的速度与温度。",{"name":83,"@type":74,"acceptedAnswer":84},"该方法在结果上与 CFD 如何对比？是否提升了效率？",{"text":85,"@type":77},"机器学习预测与 CFD 输出高度吻合，同时计算时间可降低到原来的量级，从而加速冷喷涂过程设计。",{"name":87,"@type":74,"acceptedAnswer":88},"该框架是否只适用于掩模（masked）冷喷涂？",{"text":89,"@type":77},"虽然框架针对掩模设置开发，但文中指出其能够方便地推广到未掩模（unmasked）的冷喷涂配置。","https://schema.org",{"og:url":52,"og:type":92,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":94,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":97},[98,102,106,110,115,120,125,128,133,136,140],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Story & 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