About

Enrique Del Castillo is a Distinguished Professor and Professor of Statistics at Penn State University. His research focuses on statistical methods and their applications, contributing to the fields of engineering and manufacturing. As a faculty member in the Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, he is involved in advancing research in engineering statistics and machine learning, among other areas. His work supports the department's mission of innovation and excellence in research, education, and outreach.

Research topics

• Machine Learning
• Computer Science
• Artificial Intelligence
• Mathematics
• Statistics
• Econometrics

Selected publications

• Practical Implementation of an End-to-End Methodology for SPC of 3-D Part Geometry: A Case Study

  arXiv (Cornell University) · 2025-04-11

  preprintOpen accessSenior author

  Del Castillo and Zhao (2020, 2021, 2022, 2024) have recently proposed a new methodology for the Statistical Process Control (SPC) of discrete parts whose 3-dimensional (3D) geometrical data are acquired with non-contact sensors. The approach is based on monitoring the spectrum of the Laplace-Beltrami (LB) operator of each scanned part estimated using finite element methods (FEM). The spectrum of the LB operator is an intrinsic summary of the geometry of a part, independent of the ambient space. Hence, registration of scanned parts is unnecessary when comparing them. The primary goal of this case study paper is to demonstrate the practical implementation of the spectral SPC methodology through multiple examples using real scanned parts acquired with an industrial-grade laser scanner, including 3D printed parts and commercial parts. We discuss the scanned mesh preprocessing needed in practice, including the type of remeshing found to be most beneficial for the FEM computations. For each part type, both the "phase I" and "phase II" stages of the spectral SPC methodology are showcased. In addition, we provide a new principled method to determine the number of eigenvalues of the LB operator to consider for efficient SPC of a given part geometry, and present an improved algorithm to automatically define a region of interest, particularly useful for large meshes. Computer codes that implement every method discussed in this paper, as well as all scanned part datasets used in the case studies, are made available and explained in the supplementary materials.

  PublisherDOI

• An AI Approach for Learning the Spectrum of the Laplace-Beltrami Operator

  ArXiv.org · 2025-07-09

  preprintOpen accessSenior author

  The spectrum of the Laplace-Beltrami (LB) operator is central in geometric deep learning tasks, capturing intrinsic properties of the shape of the object under consideration. The best established method for its estimation, from a triangulated mesh of the object, is based on the Finite Element Method (FEM), and computes the top k LB eigenvalues with a complexity of O(Nk), where N is the number of points. This can render the FEM method inefficient when repeatedly applied to databases of CAD mechanical parts, or in quality control applications where part metrology is acquired as large meshes and decisions about the quality of each part are needed quickly and frequently. As a solution to this problem, we present a geometric deep learning framework to predict the LB spectrum efficiently given the CAD mesh of a part, achieving significant computational savings without sacrificing accuracy, demonstrating that the LB spectrum is learnable. The proposed Graph Neural Network architecture uses a rich set of part mesh features - including Gaussian curvature, mean curvature, and principal curvatures. In addition to our trained network, we make available, for repeatability, a large curated dataset of real-world mechanical CAD models derived from the publicly available ABC dataset used for training and testing. Experimental results show that our method reduces computation time of the LB spectrum by approximately 5 times over linear FEM while delivering competitive accuracy.

  PublisherOA PDFDOI

• Monitoring 3D Lattice Structures in Additive Manufacturing Using Topological Data Analysis

  ArXiv.org · 2025-10-10

  preprintOpen accessSenior author

  We present a new method for the statistical process control of lattice structures using tools from Topological Data Analysis. Motivated by applications in additive manufacturing, such as aerospace components and biomedical implants, where hollow lattice geometries are critical, the proposed framework is based on monitoring the persistent homology properties of parts. Specifically, we focus on homological features of dimensions zero and one, corresponding to connected components and one-dimensional loops, to characterize and detect changes in the topology of lattice structures. A nonparametric hypothesis testing procedure and a control charting scheme are introduced to monitor these features during production. Furthermore, we conduct extensive run-length analysis via various simulated but real-life lattice-structured parts. Our results demonstrate that persistent homology is well-suited for detecting topological anomalies in complex geometries and offers a robust, intrinsically geometrical alternative to other SPC methods for mesh and point data.

  PublisherOA PDFDOI

• Sex-specific nutritional requirements of mating in insects with contrasting mating systems

  University of Regensburg Publication Server (University of Regensburg) · 2025-01-01

  articleOpen access

  Fitness of most animals is affected by the amount and ratio of nutrients they consume. Therefore, maximizing fitness relies on consumers fine-tuning their intake towards a specific nutritional target. However, mating might alter this target because the nutrient ratio that maximizes reproductive investment often differs from ratios that elevate the expression of other fitness traits, e.g. survival and immunity. Therefore, consumers may be under selection to shift their intake towards nutrient ratios that promote reproductive success only when the likelihood of mating is high or after mating activity. Here, we tested how mating affects total macronutrient intake and the protein-to-carbohydrate ratio consumed by males and females given a dietary choice. Three insect species, namely Australian field crickets, Teleogryllus commodus, decorated crickets, Gryllodes sigillatus, and cockroaches, Nauphoeta cinerea, were studied. Males in these species differ in the traits they use to attract females and in postcopulatory sexual selection, while females differ in the timing and magnitude of offspring investment. Despite these differences, mating triggered increased macronutrient intake in females across all species, while male intake remained unchanged. This elevated consumption indicates that mating increases the energetic demands of females more than males. Neither sex altered the nutrient ratio consumed after mating, despite nutrient ratios mediating trade-offs between aspects of reproduction, e.g. sexual display versus sperm production, and other life-history traits, e.g. survival, in these species. We speculate that this is because selection skews nutrient regulation strategies towards ratios that promote reproductive success, and mating does not trigger deviation from these relatively fixed courses. In addition, the magnitude and direction of sex differences in protein and carbohydrate intake as well as how tightly each sex regulates their macronutrient intake, differed between species. We discuss what this suggests about species-specific physiology and the costs of reproduction.

  PublisherOA PDFDOI

• Practical implementation of an End-to-end methodology for SPC of 3-D part geometry: A case study

  Journal of Quality Technology · 2025-07-23 · 1 citations

  articleOpen accessSenior authorCorresponding

  Del Castillo and Zhao (2020, 2021, 2022, 2024) have recently proposed a new methodology for the Statistical Process Control (SPC) of discrete parts whose 3-dimensional (3D) geometrical data are acquired with non-contact sensors. The approach is based on monitoring the spectrum of the Laplace-Beltrami (LB) operator of each scanned part estimated using finite element methods (FEM). The spectrum of the LB operator is an intrinsic summary of the geometry of a part, independent of the ambient space. Hence, registration of scanned parts is unnecessary when comparing them. The primary goal of this case study paper is to demonstrate the practical implementation of the spectral SPC methodology through multiple examples using real scanned parts acquired with an industrial-grade laser scanner, including 3D printed parts and commercial parts. We discuss the scanned mesh preprocessing needed in practice, including the type of remeshing found to be most beneficial for the FEM computations. For each part type, both the "phase I" and "phase II" stages of the spectral SPC methodology are showcased. In addition, we provide a new principled method to determine the number of eigenvalues of the LB operator to consider for efficient SPC of a given part geometry, and present an improved algorithm to automatically define a region of interest, particularly useful for large meshes. Computer codes that implement every method discussed in this paper, as well as all scanned part datasets used in the case studies, are made available and explained in the supplementary materials.

  PublisherOA PDFDOI

• Registration-Free Localization of Defects in Three-Dimensional Parts from Mesh Metrology Data Using Functional Maps

  INFORMS Journal on Data Science · 2023-08-16 · 3 citations

  articleSenior author

  We consider a common problem occurring after using a statistical process control (SPC) method based on three-dimensional measurements: locate where on the surface of the part that triggered an out-of-control alarm there is a significant shape difference with respect to either an in-control part or its nominal (computer-aided design (CAD)) design. In the past, only registration-based solutions existed for this problem, which first orient and locate the part and its nominal design under the same frame of reference. Recently, spectral Laplacian methods have been proposed for the SPC of discrete parts and their measured surface meshes. These techniques provide an intrinsic solution to the SPC problem: that is, a solution exclusively based on data whose coordinates lie on the surfaces without making reference to their ambient space, thus avoiding registration. Registration-free methods avoid the computationally expensive, nonconvex registration step needed to align the parts as required by previous methods, eliminating registration errors, and they are important in industry because of the increasing use of portable noncontact scanners. In this paper, we first present a new registration-free solution to the post-SPC part defect localization problem. The approach uses a spectral decomposition of the Laplace–Beltrami operator in order to construct a functional map between the CAD and measured manifolds to locate defects on the suspected part. A computational complexity analysis demonstrates the approach scales better with the mesh size and is more stable than a registration-based approach. To reduce computational expense, a new mesh partitioning algorithm is presented to find a region of interest on the surface of the part where defects are more likely to exist. The functional map method involves a large number of point-to-point comparisons based on noisy measurements, and a new statistical thresholding method used to filter the false positives in the underlying massive multiple comparisons problem is also provided. History: Bianca Maria Colosimo served as the senior editor for this article. Funding: This research was partially funded by the National Science Foundation [Grant CMMI 2121625]. Data Ethics & Reproducibility Note: There are no data ethics considerations. The code capsule is available on Code Ocean at https://codeocean.com/capsule/4615101/tree/v1 and in the e-Companion to this article (available https://doi.org/10.1287/ijds.2023.0030 ).

  PublisherDOI

• Beauty or function? The opposing effects of natural and sexual selection on cuticular hydrocarbons in male black field crickets

  Journal of Evolutionary Biology · 2023-08-03 · 10 citations

  articleOpen access

  Although many theoretical models of male sexual trait evolution assume that sexual selection is countered by natural selection, direct empirical tests of this assumption are relatively uncommon. Cuticular hydrocarbons (CHCs) are known to play an important role not only in restricting evaporative water loss but also in sexual signalling in most terrestrial arthropods. Insects adjusting their CHC layer for optimal desiccation resistance is often thought to come at the expense of successful sexual attraction, suggesting that natural and sexual selection are in opposition for this trait. In this study, we sampled the CHCs of male black field crickets (Teleogryllus commodus) using solid-phase microextraction and then either measured their evaporative water loss or mating success. We then used multivariate selection analysis to quantify the strength and form of natural and sexual selection targeting male CHCs. Both natural and sexual selection imposed significant linear and stabilizing selection on male CHCs, although for very different combinations. Natural selection largely favoured an increase in the total abundance of CHCs, especially those with a longer chain length. In contrast, mating success peaked at a lower total abundance of CHCs and declined as CHC abundance increased. However, mating success did improve with an increase in a number of specific CHC components that also increased evaporative water loss. Importantly, this resulted in the combination of male CHCs favoured by natural selection and sexual selection being strongly opposing. Our findings suggest that the balance between natural and sexual selection is likely to play an important role in the evolution of male CHCs in T. commodus and may help explain why CHCs are so divergent across populations and species.

  PublisherOA PDFDOI

• Author response for "Beauty or function? The opposing effects of natural and sexual selection on cuticular hydrocarbons in male black field crickets"

  2023-04-21

  peer-review
  PublisherDOI

• Ovarian apoptosis is regulated by carbohydrate intake but not by protein intake in speckled cockroaches

  Journal of Insect Physiology · 2022-10-26 · 3 citations

  articleOpen access

  When the likelihood of reproducing successfully is low, any prior investment in developing oocytes may be wasted. One means of recouping this investment is oosorption – where ova are absorbed and resources salvaged so they can be re-allocated to other traits. Food-limited female speckled cockroaches (Nauphoeta cinerea) appear to use this strategy. However, it is unclear if total food intake or the availability of specific nutrients induces this process. Here, we used the geometric framework of nutrition to determine how protein, carbohydrate and energy intake affect levels of ovarian apoptosis and necrosis (controlled versus uncontrolled cell death) in the terminal oocytes of female N. cinerea. We then compare the effects of nutrient intake on apoptosis (a key step towards oosorption) and offspring production to better understand the relationship between diet, apoptosis and female fitness. We found that even when food was abundant, females experienced high levels of apoptosis if their diet lacked carbohydrate. Necrosis was reduced when energy intake was high, but largely irrespective of nutrient ratio. Offspring production peaked on a low protein, high carbohydrate nutrient ratio (1P:7.96C), similar to that which minimized apoptosis (1P:7.34C) but not in the region of nutrient space that minimized necrosis. Thus, females consuming an ideal nutrient blend for reproduction can invest heavily in their current brood without needing to salvage nutrients from developing ova. However, offspring production was more dependent on carbohydrate consumption than apoptosis was, suggesting that the importance of carbohydrate in reproduction goes beyond regulating oosorption. This reliance on carbohydrate for female reproduction may reflect the unusual reproductive and nutritional physiology of speckled cockroaches; attributes that make this species an exciting model for understanding how diet regulates reproduction.

  PublisherDOI

• Carbohydrate But Not Protein Limitation Induces Ovarian Apoptosis in Speckled Cockroaches

  SSRN Electronic Journal · 2022-01-01

  articleOpen access
  PublisherDOI

Recent grants

• On-line Profile-to-Profile Process Adjustment for Robust Parameter Design Scenarios

  NSF · $230k · 2008–2012

• High Dimensional Statistical Inference in Flexible Response Surface Models for Product Formulation

  NSF · $271k · 2016–2020

• Collaborative Research: Active Statistical Learning: Ensembles, Manifolds, and Optimal Experimental Design

  NSF · $175k · 2015–2019

Frequent coauthors

• Douglas C. Montgomery

  24 shared

• Bianca Maria Colosimo

  Politecnico di Milano

  17 shared

• John J. Peterson

  Quality Research

  15 shared

• Suntara Cahya

  Eli Lilly (United States)

  11 shared

• John Hunt

  Western Sydney University

  10 shared

• Rong Pan

  10 shared

• George C. Runger

  Arizona State University

  9 shared

• Ramkumar Rajagopal

  9 shared

Awards & honors

• Enrique Del Castillo Distinguished Professor