About

Hector D. Ceniceros is a faculty member in the Department of Mathematics at the University of California, Santa Barbara. His specialization is in Applied Mathematics. He is based in South Hall, Room 6607, and his office hours are Monday through Friday from 9-12 and 1-4. His contact information includes an email address (hdc@math.ucsb.edu), a phone number (805-893-3462), and a fax number (805-893-2385).

Research topics

• Computer Science
• Artificial Intelligence
• Algorithm
• Theoretical computer science
• Medicine
• Statistical physics
• Mathematical optimization
• Quantum mechanics
• Mathematics
• Physics

Selected publications

• Machine-learning accelerated density-explicit polymer field theory simulations

  The Journal of Chemical Physics · 2026-01-02

  article

  Recently, the density-explicit framework, which describes the thermodynamic properties of multicomponent polymer systems as functionals of both auxiliary and density fields, has attracted growing interest in polymer field theory simulations. This is due to the flexibility of the framework in accommodating various forms of intermolecular potentials, and in particular, the easy generalization to many-body interactions beyond pair potentials. However, numerical simulations based on the formalism are generally more expensive owing to the increased number of fields, compared to the conventional auxiliary field framework. In this work, we develop deep neural networks with efficient low-dimensional and largely local feature representations that are applicable across different spatial resolutions and dimensions to accelerate polymer field theory simulations based on this framework. Our results may serve as a stepping stone toward accurate and efficient prediction of the phase behavior of complex block copolymer mesophases, as well as a blueprint for developing machine learning-assisted field theoretic simulation tools for the computational study of polymers and soft matter systems more broadly.

  PublisherDOI

• Machine-learning accelerated density-explicit polymer field theory simulations

  AIP Publishing · 2026-01-01

  otherOpen accessSenior author

  Recently, the density-explicit framework that describes thermodynamic properties of multicomponent polymer systems as functionals of both auxiliary and density fields has attracted growing interest in polymer field theory simulations. This is due to the flexibility of the framework in accommodating various forms of intermolecular potentials, and in particular, the easy generalization to many-body interactions beyond pair potentials. However, numerical simulations based on the formalism are generally more expensive owing to the increased number of fields, compared to the conventional auxiliary field framework. In this work, we develop deep neural networks with efficient low-dimensional and largely local feature representations that are applicable across different spatial resolutions and dimensions to accelerate polymer field theory simulations based on this framework. Our results may serve as a stepping stone toward accurate and efficient prediction of the phase behavior of complex block copolymer mesophases, as well as a blueprint for developing machine learning-assisted field theoretic simulation tools for the computational study of polymers and soft matter systems more broadly.

  PublisherDOI

• Supplementary Material PDF

  AIP Publishing · 2026-01-02

  articleOpen access

  Supplementary Material containing text and images.

  PublisherDOI

• Machine-learning accelerated density-explicit polymer field theory simulations

  AIP Publishing · 2026-01-01

  otherOpen accessSenior author

  Recently, the density-explicit framework that describes thermodynamic properties of multicomponent polymer systems as functionals of both auxiliary and density fields has attracted growing interest in polymer field theory simulations. This is due to the flexibility of the framework in accommodating various forms of intermolecular potentials, and in particular, the easy generalization to many-body interactions beyond pair potentials. However, numerical simulations based on the formalism are generally more expensive owing to the increased number of fields, compared to the conventional auxiliary field framework. In this work, we develop deep neural networks with efficient low-dimensional and largely local feature representations that are applicable across different spatial resolutions and dimensions to accelerate polymer field theory simulations based on this framework. Our results may serve as a stepping stone toward accurate and efficient prediction of the phase behavior of complex block copolymer mesophases, as well as a blueprint for developing machine learning-assisted field theoretic simulation tools for the computational study of polymers and soft matter systems more broadly.

  PublisherDOI

• Supplementary Material PDF

  AIP Publishing · 2026-01-02

  articleOpen access

  Supplementary Material containing text and images.

  PublisherDOI

• Projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles

  Physical review. E · 2024-12-27 · 1 citations

  articleOpen access

  We introduce a projected complex Langevin (CL) numerical sampling method-a fictitious Langevin dynamics scheme that uses numerical projection to sample a constrained stationary distribution with highly oscillatory character. Despite the complex-valued degrees of freedom and associated sign problem, the projected CL method succeeds as a natural extension of real-valued projected Langevin processes. In the newly proposed method, complex-valued Lagrange multipliers are determined to enforce constraints to machine precision at each iteration. To illustrate the efficacy of this approach, we adapt the projected CL method to sample coherent state quantum field theories describing interacting Bose gases, which are realized in modern cold-atom experiments. We apply projected CL to two scenarios with holomorphic constraints, namely the canonical and microcanonical ensembles, and we show that projected CL reproduces the correct thermodynamic observables. We further observe improved numerical stability and accuracy at larger time steps when compared to the previous state-of-the-art method for performing constrained CL sampling.

  PublisherOA PDFDOI

• Machine learning and polymer self-consistent field theory in two spatial dimensions

  The Journal of Chemical Physics · 2023 · 10 citations

  • Computer Science
  • Artificial Intelligence
  • Computer Science

  A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in the work of Xuan et al. [J. Comput. Phys. 443, 110519 (2021)]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

  PublisherDOI

• Stochastic Delay Differential Games: Financial Modeling and Machine Learning Algorithms

  arXiv (Cornell University) · 2023-07-12 · 1 citations

  preprintOpen access

  In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction and delayed effects are often desired features in a model, but are introduced at the expense of increased dimensionality of the problem. This increased dimensionality is especially significant as that arising from the number of players is coupled with the potential infinite dimensionality caused by the delay. Our approach involves parameterizing the controls of each player using distinct recurrent neural networks. These recurrent neural network-based controls are then trained using a modified version of Brown's fictitious play, incorporating deep learning techniques. To evaluate the effectiveness of our methodology, we test it on finance-related problems with known solutions. Furthermore, we also develop new problems and derive their analytical Nash equilibrium solutions, which serve as additional benchmarks for assessing the performance of our proposed deep learning approach.

  PublisherOA PDFDOI

• Machine Learning and Polymer Self-Consistent Field Theory in Two Spatial Dimensions

  arXiv (Cornell University) · 2022-12-16

  preprintOpen access

  A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in [1]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network (CNN) is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

  PublisherOA PDFDOI

• Pandemic Control, Game Theory, and Machine Learning

  Notices of the American Mathematical Society · 2022-11-09 · 3 citations

  articleOpen accessSenior author
  PublisherDOI

Recent grants

• Innovative methods for the dynamics of immersed structures in complex fluids

  NSF · $401k · 2010–2014

• Adaptive, Non-stiff, and Stochastic Methods for Phase Field Fluid Models

  NSF · $225k · 2006–2009

• Machine Learning-Enabled Self-Consistent Field Theory for Soft Materials

  NSF · $273k · 2024–2027

• Multiscale Approaches for the Dynamics and Rheology of Magnetic Fluids

  NSF · $405k · 2013–2017

• Smart Data Approaches for the Inverse Design of Soft Materials

  NSF · $200k · 2018–2022

Frequent coauthors

• Carlos J. García‐Cervera

  University of California, Santa Barbara

  26 shared

• Glenn H. Fredrickson

  University of California, Santa Barbara

  21 shared

• Alexandre M. Roma

  Universidade de São Paulo

  19 shared

• L. Gary Leal

  University of California, Santa Barbara

  12 shared

• Rudimar Luiz Nós

  Universidade Tecnológica Federal do Paraná

  12 shared

• David H. Klein

  11 shared

• Kris T. Delaney

  University of California, Santa Barbara

  11 shared

• Thomas Y. Hou

  California Institute of Technology

  6 shared