About

Professor Konstantinos Spiliopoulos is a member of the Applied Mathematics and Probability and Statistics research groups at Boston University. He holds the position of Professor and Director of Statistics within the department. His academic and professional focus is on applied mathematics, with particular emphasis on probability and statistics. For more information about Professor Spiliopoulos, please see his personal website.

Research topics

• Computer Science
• Statistical physics
• Mathematics
• Mathematical analysis
• Thermodynamics
• Applied mathematics
• Physics
• Pure mathematics
• Statistics

Selected publications

• Mean-field analysis of latent variable process models on dynamically evolving graphs with feedback effects

  Probability Theory and Related Fields · 2026-04-28

  preprintOpen access
  PublisherOA PDFDOI

• Who's Afraid of Coalition Talk? Mapping Polarization Among Northern Europe's Cabinets in a Coevolving Latent Space

  SSRN Electronic Journal · 2026-01-01

  preprintOpen access
  PublisherDOI

• A Macroscopically Consistent Reactive Langevin Dynamics Model

  ArXiv.org · 2025-01-16

  preprintOpen access

  Overview ReactLD.jl is a Julia package for performing stochastic simulations of particle-based reactive Brownian and Langevin dynamics using the Stochastic Simulation Algorithm (SSA). This repository accompanies the experiments presented in the paper "A Macroscopically Consistent Reactive Langevin Dynamics Model." In this work, we focus on simulating particle systems governed by both Brownian/Langevin dynamics and reversible bimolecular reactions of the form A + B ⇌ C. The package tracks individual particles in continuous space, capturing their stochastic motion, interactions, and reaction events over time. The framework is general and extensible to more complex reaction networks — see our paper for details. Abstract Particle-based stochastic reaction-diffusion (PBSRD) models are a popular approach for capturing stochasticity in reaction and transport processes across biological systems. In some contexts, the overdamped approximation inherent in such models may be inappropriate, necessitating the use of more microscopic Langevin Dynamics models for spatial transport. In this work we develop a novel particle-based Reactive Langevin Dynamics (RLD) model, with a focus on deriving reactive interaction kernels that are consistent with the physical constraint of detailed balance of reactive fluxes at equilibrium. We demonstrate that, to leading order, the overdamped limit of the resulting RLD model corresponds to the volume reactivity PBSRD model, of which the well-known Doi model is a particular instance. Our work provides a step towards systematically deriving PBSRD models from more microscopic reaction models, and suggests possible constraints on the latter to ensure consistency between the two physical scales.

  PublisherOA PDFDOI

• Convergence Analysis of Real-time Recurrent Learning (RTRL) for a class of Recurrent Neural Networks

  ArXiv.org · 2025-01-14

  preprintOpen accessSenior author

  Recurrent neural networks (RNNs) are commonly trained with the truncated backpropagation-through-time (TBPTT) algorithm. For the purposes of computational tractability, the TBPTT algorithm truncates the chain rule and calculates the gradient on a finite block of the overall data sequence. Such approximation could lead to significant inaccuracies, as the block length for the truncated backpropagation is typically limited to be much smaller than the overall sequence length. In contrast, Real-time recurrent learning (RTRL) is an online optimization algorithm which asymptotically follows the true gradient of the loss on the data sequence as the number of sequence time steps $t \rightarrow \infty$. RTRL forward propagates the derivatives of the RNN hidden/memory units with respect to the parameters and, using the forward derivatives, performs online updates of the parameters at each time step in the data sequence. RTRL's online forward propagation allows for exact optimization over extremely long data sequences, although it can be computationally costly for models with large numbers of parameters. We prove convergence of the RTRL algorithm for a class of RNNs. The convergence analysis establishes a fixed point for the joint distribution of the data sequence, RNN hidden layer, and the RNN hidden layer forward derivatives as the number of data samples from the sequence and the number of training steps tend to infinity. We prove convergence of the RTRL algorithm to a stationary point of the loss. Numerical studies illustrate our theoretical results. One potential application area for RTRL is the analysis of financial data, which typically involve long time series and models with small to medium numbers of parameters. This makes RTRL computationally tractable and a potentially appealing optimization method for training models. Thus, we include an example of RTRL applied to limit order book data.

  PublisherOA PDFDOI

• On the large-time behaviour of affine Volterra processes

  Stochastics · 2025-09-04

  articleSenior author
  PublisherDOI

• Mean field limits of particle-based stochastic reaction-drift-diffusion models^*

  Nonlinearity · 2025-01-07

  articleOpen accessSenior authorCorresponding

  Abstract We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued stochastic processes (MVSPs), which describe the evolution of the singular, stochastic concentration fields of each chemical species. The mean field large population limit of such models is derived and proven, giving coarse-grained deterministic partial integro-differential equations (PIDEs) for the limiting deterministic concentration fields’ dynamics. We generalize previous studies on the mean field limit of models involving only diffusive motion, with care to formulating the MVSP representation to ensure detailed balance of reversible reactions in the presence of potentials. Our work illustrates the more general set of PIDEs that arise in the mean field limit, demonstrating that the limiting macroscopic reactive interaction terms for reversible reactions obtain additional nonlinear concentration-dependent coefficients compared to the purely diffusive case. Numerical studies are presented which illustrate that two-body repulsive potential interactions can have a significant impact on the reaction dynamics, and also demonstrate the empirical numerical convergence of solutions to the PBSRDD model to the derived mean field PIDEs as the population size increases.

  PublisherOA PDFDOI

• Uniform attraction and exit problems for stochastic damped wave equations

  ArXiv.org · 2025-02-03

  preprintOpen accessSenior author

  We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet boundary conditions, continuous initial position and distributional initial velocity. In the first part of this work, we study the corresponding deterministic dynamics and prove that certain neighborhoods of asymptotically stable equilibria are uniformly attracting in the topology of uniform convergence. Then, we consider exit problems for local solutions of the stochastic damped wave equations from bounded domains $D$ of uniform attraction. Using tools from large deviations along with novel controllability results, we obtain logarithmic asymptotics for exit times and exit places, in the vanishing noise limit, that are expressed in terms of the corresponding quasipotential. In doing so, we develop arguments that take into account the lack of both smoothing and exact controllability that are inherent to the problem at hand. Moreover, our exit time results provide asymptotic lower bounds for the mean explosion time of local solutions. We introduce a novel notion of "regular" boundary points allowing to avoid the question of boundary smoothness in infinite dimensions and leading to the proof of a large deviations lower bound for the exit place. We illustrate this notion by providing explicit examples for different classes of domains $D$. Conditions under which lower and upper bounds for exit time and exit place logarithmic asymptotic hold, are also presented. In addition, we obtain deterministic stability results for linear damped wave equations that are of independent interest.

  PublisherOA PDFDOI

• Global Convergence of Adjoint-Optimized Neural PDEs

  ArXiv.org · 2025-06-16

  preprintOpen accessSenior author

  Many engineering and scientific fields have recently become interested in modeling terms in partial differential equations (PDEs) with neural networks, which requires solving the inverse problem of learning neural network terms from observed data in order to approximate missing or unresolved physics in the PDE model. The resulting neural-network PDE model, being a function of the neural network parameters, can be calibrated to the available ground truth data by optimizing over the PDE using gradient descent, where the gradient is evaluated in a computationally efficient manner by solving an adjoint PDE. These neural PDE models have emerged as an important research area in scientific machine learning. In this paper, we study the convergence of the adjoint gradient descent optimization method for training neural PDE models in the limit where both the number of hidden units and the training time tend to infinity. Specifically, for a general class of nonlinear parabolic PDEs with a neural network embedded in the source term, we prove convergence of the trained neural-network PDE solution to the target data (i.e., a global minimizer). The global convergence proof poses a unique mathematical challenge that is not encountered in finite-dimensional neural network convergence analyses due to (i) the neural network training dynamics involving a non-local neural network kernel operator in the infinite-width hidden layer limit where the kernel lacks a spectral gap for its eigenvalues and (ii) the nonlinearity of the limit PDE system, which leads to a non-convex optimization problem in the neural network function even in the infinite-width hidden layer limit (unlike in typical neural network training cases where the optimization problem becomes convex in the large neuron limit). The theoretical results are illustrated and empirically validated by numerical studies.

  PublisherOA PDFDOI

• Stochastic Gradient Descent-based Inference for Dynamic Network Models with Attractors

  Journal of Computational and Graphical Statistics · 2025-01-06

  article

  In Coevolving Latent Space Networks with Attractors (CLSNA) models, nodes in a latent space represent social actors, and edges indicate their dynamic interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing from dynamical systems theory. However, CLSNA reliance on MCMC estimation makes scaling difficult, and the requirement for nodes to be present throughout the study period limit practical applications. We address these issues by (i) introducing a Stochastic gradient descent (SGD) parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave over time. Simulation results show that our extensions result in little loss of accuracy compared to MCMC, but can scale to much larger networks. We apply our approach to the longitudinal social networks of members of US Congress on the social media platform X. Accounting for node dynamics overcomes selection bias in the network and uncovers uniquely and increasingly repulsive forces within the Republican Party. Supplemental materials for the article are available online.

  PublisherDOI

• Stochastic gradient descent-based inference for dynamic network models with attractors

  arXiv (Cornell University) · 2024-03-11

  preprintOpen access

  In Coevolving Latent Space Networks with Attractors (CLSNA) models, nodes in a latent space represent social actors, and edges indicate their dynamic interactions. Attractors are added at the latent level to capture the notion of attractive and repulsive forces between nodes, borrowing from dynamical systems theory. However, CLSNA reliance on MCMC estimation makes scaling difficult, and the requirement for nodes to be present throughout the study period limit practical applications. We address these issues by (i) introducing a Stochastic gradient descent (SGD) parameter estimation method, (ii) developing a novel approach for uncertainty quantification using SGD, and (iii) extending the model to allow nodes to join and leave over time. Simulation results show that our extensions result in little loss of accuracy compared to MCMC, but can scale to much larger networks. We apply our approach to the longitudinal social networks of members of US Congress on the social media platform X. Accounting for node dynamics overcomes selection bias in the network and uncovers uniquely and increasingly repulsive forces within the Republican Party.

  PublisherOA PDFDOI

Recent grants

• Monte Carlo Methods, Metastability and Stochastic Processes with Multiple Scales

  NSF · $113k · 2013–2017

• CAREER: Multiscale stochastic processes, Monte Carlo Methods and Irreversibility

  NSF · $480k · 2016–2022

• Multiscale Effects and Tail Events for Infinite-Dimensional Processes and Interacting Particle Systems

  NSF · $256k · 2021–2025

Frequent coauthors

• Justin Sirignano

  University of Oxford

  46 shared

• Scott Robertson

  20 shared

• Richard B. Sowers

  University of Illinois Urbana-Champaign

  19 shared

• Michael Salins

  17 shared

• Kay Giesecke

  Stanford University

  16 shared

• Siragan Gailus

  14 shared

• Michail Anthropelos

  Piraeus Bank

  12 shared

• Paul Dupuis

  11 shared