This workshop will bring together researchers interested in the phenomenon of emergence in complex systems of interacting agents. Such systems are ubiquitous in science and engineering, and include the flocking of birds and schooling of fish, celestial dynamics, phototaxis in bacterial populations, consensus formation, and the coordination of unmanned aerial vehicles. As complex dynamical systems, their study is highly nontrivial, and relies on a wide range of techniques, including tools from mathematical analysis, data science, and control theory. The goal of this workshop is to assemble researchers from these disciplines to present recent work, and to foster interdisciplinary collaborations between mathematicians, data scientists, and control theorists. Researchers will gain new perspectives and insights on the phenomenon of emergence, as well as new tools to tackle the challenging problem of modeling and predicting complex behavior.
Funding
NOTE: All funding for this workshop has been allocated.
Poster Session
This workshop will include a poster session. In order to propose a poster, you must first register for the workshop, and then submit a proposal using the form that will become available on this page after you register. The registration form should not be used to propose a poster.
The deadline for proposing is February 16, 2025. If your proposal is accepted, you should plan to attend the event in-person.
Benoit Bonnet-Weill
CentraleSupelec, University of Paris-Saclay
D
B
David Bortz
University of Colorado, Boulder
F
B
Francesco Bullo
University of California, Santa Barbara
A
B
Andreas Buttenschoen
University of Massachusetts, Amherst
M
D
Maria D’Orgsona
California State University Northridge
X
G
Xiaoqian Gong
Amherst College
Q
L
Qin Li
University of Wisconsin, Madison
F
L
Fei Lu
Johns Hopkins University
M
M
Mauro Maggioni
Johns Hopkins University
N
M
Niall Mangan
Northwestern University
N
M
Naoki Masuda
SUNY Buffalo
J
P
Jan Peszek
University of Warsaw
B
P
Benedetto Piccoli
Rutgers University
N
R
Nancy Rodriguez
University of Colorado, Boulder
R
S
Ruiwen Shu
University of Georgia
R
S
Roman Shvydkoy
University of Illinois at Chicago
E
T
Eitan Tadmor
University of Maryland
C
T
Changhui Tan
University of South Carolina
K
T
Konstantina Trivisa
University of Maryland, College Park
E
Z
Ewelina Zatorska
University of Warwick
Schedule
Monday, March 17, 2025
8:30-9:30 CDT
Welcome and Breakfast
9:30-10:15 CDT
Existence and long time behavior of weak solutions to the Fokker-Planck-Alignment models
Speaker: Roman Shvydkoy (University of Illinois at Chicago)
In this talk we address global existence of weak solutions, their regularization, and global relaxation
to Maxwellian for a broad class of Fokker-Planck-Alignment models which appear in collective dynamics. The main feature of these results, as opposed to previously known ones, is the lack of regularity or no-vacuum requirements on the initial data. With a particular application to the classical kinetic Cucker-Smale model, we demonstrate that any bounded data with finite energy, $(1+ |v|^2) f_0 \in L^1, f_0 \in L^\infty$, and finite higher moment $|v|^q f \in L^2$, $q \gg 2$ , gives rise to a global instantly smooth solution, satisfying entropy equality and relaxing exponentially fast.
The results are achieved through the use of a new thickness-based renormalization, which circumvents the problem of degenerate diffusion in non-perturbative regime.
10:20-11:05 CDT
TBA
Speaker: Nicole Abaid (Virginia Polytechnic Institute & State University (Virginia Tech))
11:05-11:35 CDT
Coffee Break
11:40-12:25 CDT
Immigration and integration in changing societies
Speaker: Maria D’Orsogna (California State University Northridge)
"The social integration of newcomers into existing communities has become an issue of
major concern, especially as large-scale migration becomes more common worldwide,
due to wars, famine or as individuals seek better economic opportunities.
While newcomers can strengthen the workforce and bring in cultural diversity, societal
tensions due to different cultural norms or competition for limited resources may also arise.
We use a dynamic network model of interacting newcomer and native agents
characterized by evolving cultural norms who aim to optimize their socioeconomic prosperity.
Network links evolve through game-theoretic rules that aim to maximize agents' payoff functions
and through opinion dynamics whereby agents seek cultural acceptance.
We identify the conditions under which cooperative/integrated or uncooperative/segregated societies arise.
Within our model, the main predictor of integration is the timescale associated with cultural adjustment relative to socioeconomic linking. Fast cultural adjustment, for both native and newcomer agents leads
to the establishment of cross group connections that can be sustained over long times.
Conversely, fast socioeconomic linking leads to the irreversible formation of isolated enclaves,
as natives and newcomers maximize their payoffs through in-group connections."
12:30-14:00 CDT
Lunch Break
14:00-14:45 CDT
TBA
Speaker: Andreas Buttenschoen (University of Massachusetts Amherst)
14:50-15:20 CDT
Coffee Break
15:25-16:10 CDT
Extended convexity and uniqueness of minimizers for interaction energies
Speaker: Ruiwen Shu (University of Georgia)
The linear interpolation convexity (LIC) has served as the essential condition to guarantee the uniqueness of minimizer for pairwise interaction energies. In particular, for power-law potentials $W(x) = \frac{|x|^a}{a} - \frac{|x|^b}{b}$, it is known that LIC holds for $-d \lt b \leq 2, 2 \leq a \leq 4, b \lt a, (a, b) \neq (4, 2)$. We extend the notion of LIC by requiring the energy convexity only for linear interpolation between probability measures supported on a prescribed ball. This allows us to prove the uniqueness of minimizer for power-law potentials with $a$ slightly smaller than 2 or larger than 4.
Tuesday, March 18, 2025
8:30-9:15 CDT
Sign-in/Breakfast
9:15-10:00 CDT
Early warning indicators for regime shifts in network dynamics
Speaker: Naoki Masuda (State University of New York at Buffalo)
Complex dynamical systems often show sudden major changes, or tipping points, as the system gradually changes. Examples include mass extinctions in an ecosystem, deforestation, and aggressive progression of a disease in a human body. Exploiting critical slowing down phenomena among other things, various early warning signals (EWSs) that anticipate tipping events before they occur have been developed. In fact, complex dynamical systems of our interest often form a heterogeneous network, often as a result of emergent behavior of interacting agents. How to construct EWSs in this network situation is not straightforward. We present heuristic and mathematically grounded methods to select sentinel nodes in a given network to construct good EWSs. We show that carefully chosen small subsets of nodes can anticipate transitions as well as or even better than using all the nodes under a wide variety of conditions. We further address the case in which one cannot use too many observations from each node for forming EWSs.
10:05-10:50 CDT
TBA
Speaker: Changhui Tan (University of South Carolina Columbia)
10:50-11:20 CDT
Coffee Break
11:25-12:10 CDT
Learning Interaction laws in particle- and agent-based systems
"Abstract: We consider systems of interacting agents or particles, which are commonly used for modeling across the sciences. While these systems have very high-dimensional state spaces, the laws of interaction between the agents may be quite simple, for example they may depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances, or other variables, on Euclidean spaces, manifolds, or networks. We consider this problem in the case of a finite number of agents, with observations along an increasing number of paths. We cast this as an inverse problem, discuss when this problem is well-posed, construct estimators for the interaction kernels with provably good statistically and computational properties.
We discuss the fundamental role of the geometry of the underlying space, in the cases of Euclidean space, manifolds, and networks, even in the case when the network is unknown. Finally, we consider extensions to second-order systems, more general interaction kernels, stochastic systems, and to the setting where the variables (e.g. pairwise distance) on which the interaction kernel depends are not known a priori. This is joint work with Q. Lang (Duke), F. Lu (JHU), S. Tang (UCSB), X. Wang (JHU) , M.Zhong (UH)."
12:15-12:35 CDT
Group Photo
12:35-14:00 CDT
Lunch Break
14:00-15:00 CDT
The emergence of entropy solutions for Euler alignment equations
Speaker: Eitan Tadmor (University of Maryland)
"The hydrodynamic description for emergent behavior of interacting agents is governed by Euler alignment equations, driven by different protocols of pairwise communication kernels. We survey recent results in Euler alignment dynamics with emphasis on the multi-dimensional setting.
We discuss the role of entropy inequality in selecting mono-kinetic closure for strong, non-vacuous solutions of alignment equations, we prove the existence of such strong solutions under proper sub-critical threshold conditions, and we explore related invariants which extend the 1-D notion of an “e” quantity."
15:00-16:30 CDT
Social Hour/Poster session
Wednesday, March 19, 2025
8:30-9:30 CDT
Sign-in/Breakfast
9:30-10:15 CDT
Sparse-optimization to discover dynamical systems models from data
Speaker: Niall Mangan (Northwestern University)
Building models for biological, chemical, and physical systems has traditionally relied on domain-specific intuition about which interactions and features most strongly influence a system. Alternatively, machine-learning methods are adept at finding novel patterns in large data sets and building predictive models but can be challenging to interpret in terms of or integrate with existing knowledge. Our group balances traditional modeling with data-driven methods and optimization to get the best of both worlds. Recently developed for and applied to dynamical systems, sparse optimization strategies can select a subset of terms from a library that best describes data, automatically interfering potential model structures from a broad but well-defined class. I will discuss my group’s development and application of data-driven methods for model selection to 1) recover chaotic systems models from data with hidden variables, 2) discover models for metabolic and temperature regulation in hibernating mammals, and 3) model selection for differential-algebraic-equations including chemical reaction networks and electrical grids. I’ll briefly discuss current work and roadblocks on these topics.
10:20-11:05 CDT
Self-test loss functions for learning weak-form operators and gradient flows
Speaker: Fei Lu (Johns Hopkins University)
The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge by introducing self-test loss functions, which employ test functions that depend on the unknown parameters, specifically for cases where the operator depends linearly on the unknowns. The proposed self-test loss function conserves energy for gradient flows and coincides with the expected log-likelihood ratio for stochastic differential equations. Importantly, it is quadratic, facilitating theoretical analysis of identifiability and well-posedness of the inverse problem, while also leading to efficient parametric or nonparametric regression algorithms. It is computationally simple, requiring only low-order derivatives or even being entirely derivative-free, and numerical experiments demonstrate its robustness against noisy and discrete data.
11:05-11:35 CDT
Coffee Break
11:40-12:25 CDT
Hamiltonian flow for accelerating optimization over the probability space
Speaker: Qin Li (University of Wisconsin, Madison)
12:30-14:00 CDT
Lunch Break
14:00-14:45 CDT
An efficient quantum algorithm for dissipative nonlinear partial differential equations
Speaker: Konstantina Trivisa (University of Maryland)
"Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation. Applications in fluid dynamics and epidemiology are discussed. The article ""Efficient quantum algorithm for dissipative nonlinear partial differential equations"" appeared recently in the Proceedings of the National Academy of Sciences (PNAS 2021).
Authors: J-P LIu, H. Kolden, H. Krovi, N. Loureiro, K. Trivisa and A. Childs."
14:50-15:20 CDT
Coffee Break
15:25-16:10 CDT
TBA
Speaker: David Bortz (University of Colorado, Boulder)
Thursday, March 20, 2025
8:30-9:30 CDT
Sign-in/Breakfast
9:30-10:15 CDT
TBA
Speaker: Benoit Bonnet-Weill (CentraleSupelec, University of Paris-Saclay)
10:20-11:05 CDT
Modeling Online-to-Offline Spillovers: Epidemic and Reaction-Diffusion Approaches
Speaker: Nancy Rodriguez (University of Colorado, Boulder)
With about two-thirds of the global population using social media, online interactions often influence offline events such as protests and violence. This talk presents two mathematical frameworks to model these online-to-offline spillovers. The first framework uses an epidemic-type model on networks, exploring mean field approximations to the stochastic processes and deriving reproductive numbers for these models. We also examine how network structure impacts the accuracy of these approximations. The second framework applies a reaction-diffusion model on networks to analyze the spreading speeds of traveling wave solutions. We identify parameter regimes for approximating these speeds on k-ary trees and characterize scenarios involving pushed, pulled, and pinned waves. These models provide insights into how information spreads across networks and triggers offline behaviors.
11:05-11:35 CDT
Coffee Break
11:40-12:25 CDT
Wellposeness of the nonlocal GARZ model for traffic flow
Speaker: Xiaoqian Gong (Amherst College)
"In this talk, we explore the nonlocal formulation of the generalized Aw-Rascle-Zhang (GARZ) model, a system of nonlocal hyperbolic conservation laws that governs macroscopic vehicular traffic flow. Applying the contraction mapping theorem, we prove the existence and uniqueness of weak solutions to the corresponding initial value problem over any finite time horizon. Furthermore, we investigate the stability of solutions with respect to initial data and establish the system’s maximum principle. "
12:30-14:00 CDT
Lunch Break
14:00-14:45 CDT
One-dimensional compressible Euler equations with non-local effects
Speaker: Ewelina Zatorska (University of Warwick)
This talk will be devoted to a one-dimensional model of collective motion. The considered system consists of compressible Euler equations with nonlocal interaction term playing the same role as the pressure term in fluids’ equations. I will present some of our recent results concerning existence of strong and weak solutions, long-time asymptotic of solutions, and singular limits through relative entropy method based on the two-velocity formulation.
14:50-15:20 CDT
Coffee Break
15:25-16:10 CDT
TBA
Speaker: Zahra Aminzare (University of Iowa)
Friday, March 21, 2025
8:30-9:30 CDT
Sign-in/Breakfast
9:30-10:15 CDT
Monitoring and guiding large crowds: vehicular traffic and pedestrians
We propose a multiscale optimal control problem for crowd management. The crowd is represented at the macroscopic level via mean-field equations or measure differential equations, while the control is exerted by agents. We show some results in terms of the existence of optimal controls, discuss difficulties, and compare with other approaches. Applications to control vehicular traffic via autonomous vehicles and surveillance of pedestrian crowds with drones will be presented.
10:20-11:05 CDT
TBA
Speaker: Jan Peszek (University of Warsaw)
11:05-11:35 CDT
Coffee Break
11:40-12:25 CDT
TBA
Speaker: Francesco Bullo (University of California, Santa Barbara)
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