Applied/ACMS: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
 
(102 intermediate revisions by 9 users not shown)
Line 6: Line 6:
*'''Where:''' 901 Van Vleck Hall
*'''Where:''' 901 Van Vleck Hall
*'''Organizers:'''  [https://math.wisc.edu/staff/fabien-maurice/ Maurice Fabien], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie],  
*'''Organizers:'''  [https://math.wisc.edu/staff/fabien-maurice/ Maurice Fabien], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie],  
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+join@g-groups.wisc.edu].
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+subscribe@g-groups.wisc.edu].


<br>   
<br>   


== Spring 2024  ==
== '''Spring 2025''' ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
! align="left" |Date
!align="left" | speaker
! align="left" |Speaker
!align="left" | title
! align="left" |Title
!align="left" | host(s)
! align="left" |Host(s)
|-
|-
| Feb 2
|Jan 31
|[https://people.math.wisc.edu/~chr/ Chris Rycroft] (UW)
|[https://people.math.wisc.edu/~tgchandler/ Thomas Chandler] (UW)
|''The reference map technique for simulating complex materials and multi-body interactions''
|[[#Chandler|''Fluid–structure interactions in active complex fluids'']]
|
|Spagnolie
|-
|-
| Feb 9
|Feb 7
|[https://users.flatironinstitute.org/~sweady/ Scott Weady] (Flatiron Institute)
|[https://afraser3.github.io/ Adrian Fraser] (Colorado)
|''Entropy methods in active suspensions''
|[[#Fraser|''Destabilization of transverse waves by periodic shear flows'']]
|Saverio and Laurel
|Spagnolie
|-
|-
| Feb 16
|Feb 14
|[http://stokeslet.ucsd.edu/ David Saintillan] (UC San Diego)
|[https://jrluedtke.github.io/ Jim Luedtke] (UW)
|''[[Applied/ACMS/absS24#David Saintillan (UC San Diego)|Hydrodynamics of active nematic surfaces]]''
|[[#Luedtke|Using integer programming for verification of binarized neural networks]]
|Saverio and Tom
|Spagnolie
|-
|-
| Feb 23
|Feb 21
|[https://cersonsky-lab.github.io/website/ Rose Cersonsky] (UW)
|[https://zhdankin.physics.wisc.edu/ Vladimir Zhdankin] (UW)
|''Data-driven approaches to chemical and materials sciences''
|[[#Zhdankin|Exploring astrophysical plasma turbulence with particle-in-cell methods]]
|Chris
|Spagnolie
|-
|-
| Mar 1 [4:00pm Colloquium]
|Feb 28
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT Austin)
|[https://nmboffi.github.io/ Nick Boffi] (CMU)
|''[[Applied/ACMS/absS24#Per-Gunnar Martinsson (UT-Austin)|TBA]]''
|[[#Boffi|Generative modeling with stochastic interpolants]]
|Li
|Li
|-
|-
| Mar 8
|Mar 7
|[https://www.physics.wisc.edu/directory/jorge-rogerio/ Rogerio Jorge] (UW-Madison)
|[https://sites.lsa.umich.edu/shankar-lab/ Suraj Shankar] (Michigan)
|''[[Applied/ACMS/absS24#Rogerio Jorge (UW-Madison)|The Direct Optimization Framework in Stellarator Design: Transport and Turbulence Optimization]]''
|[[#Shankar|TBA]]
|Spagnolie
|-
|Mar 14
|[https://lu.seas.harvard.edu/ Yue Lu] (Harvard) '''[Colloquium]'''
|[[#Lu|TBA]]
|Li
|Li
|-
|-
| Mar 15
|Mar 21
|[https://www.math.purdue.edu/~qi117/personal.html/ Di Qi] (Purdue University)
|[https://people.llnl.gov/vogman1 Genia Vogman] (LLNL)
|[[Applied/ACMS#diqi|Statistical Reduced-Order Models and Random Batch Method for Complex Multiscale Systems]]
|[[#Vogman|TBA]]
|Chen
|Li
|-
|-
| Mar 22
|Mar 28
|
|''Spring Break''
|
|
|
|
|-
|-
| Mar 29
|Apr 4
|Spring break
|TBA
|
|
|
|
|-
|-
| Apr 5
|Apr 11
|[https://www.jinlongwu.org/ Jinlong Wu] (UW)
|[https://meche.mit.edu/people/faculty/pierrel@mit.edu Pierre Lermusiaux] (MIT)
|''[[Applied/ACMS/absS24#Jinlong Wu (UW)|TBA]]''
|[[#Lermusiaux|TBA]]
|Saverio
|Chen
|-
|-
| Apr 12
|Apr 18
|[https://zayascaban.labs.wisc.edu/ Gabriel Zayas-Caban] (UW)
|[https://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine) '''[Colloquium]'''
|''[[Applied/ACMS/absS24#Gabriel Zayas-Caban (UW)|TBA]]''
|[[#Xin|TBA]]
|Li
|
|-
| Apr 19
|[https://www.nist.gov/people/anthony-j-kearsley Tony Kearsley] (NIST)
|''[[Applied/ACMS/absS24#Tony Kearsley (NIST)|TBA]]''
|Fabien
|-
|-
| Apr 26
|Apr 25
|[https://math.oregonstate.edu/directory/malgorzata-peszynska Malgorzata Peszynska] (Oregon State)
|[https://www-users.cse.umn.edu/~bcockbur/ Bernardo Cockburn] (Minnesota)
|''[[Applied/ACMS/absS24#Malgorzata Peszynska (Oregon State)|TBA]]''
|[[#Cockburn|''Transforming stabilization into spaces'']]
|Fabien
| Stechmann, Fabien
|-
|-
|
|May 2
|
|[https://sylviaherbert.com/ Sylvia Herbert] (UCSD)
|[[#Herbert|TBA]]
|Chen
|}
|}


== Abstracts ==
==Abstracts==


==== Chris Rycroft (UW–Madison) ====
<div id="Chandler">
Title: The reference map technique for simulating complex materials and multi-body interactions
====Thomas G. J. Chandler (UW)====
Title: Fluid-structure interactions in active complex fluids


Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented [1]. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems [2], and several examples in two and three dimensions [3] will be presented.
Fluid anisotropy is central to many biological systems, from rod-like bacteria that self-assemble into dense swarms that function as fluids, to the cell cytoskeleton where the active alignment of stiff biofilaments is crucial to cell division. Nematic liquid crystals provide a powerful model for studying these complex environments. However, large immersed bodies elastically frustrate these fluids, leading to intricate interactions. This frustration can be alleviated through body deformations, at the cost of introducing internal stresses. Additionally, active stresses, arising from particle motility or molecular activity, disrupt nematic order by driving flows. In this presentation, I will demonstrate how complex variables enable analytical solutions to a broad range of problems, offering key insights into the roles of body geometry, anchoring conditions, interaction dynamics, activity-induced flows, and body deformations in many biological settings.


# K. Kamrin, C. H. Rycroft, and J.-C. Nave, J. Mech. Phys. Solids '''60''', 1952–1969 (2012). [https://doi.org/10.1016/j.jmps.2012.06.003 <nowiki>[DOI link]</nowiki>]
<div id="Fraser">
# C. H. Rycroft ''et al.'', J. Fluid Mech. '''898''', A9 (2020). [https://doi.org/10.1017/jfm.2020.353 <nowiki>[DOI link]</nowiki>]
====Adrian Fraser (Colorado)====
# Y. L. Lin, N. J. Derr, and C. H. Rycroft, Proc. Natl. Acad. Sci. '''119''', e2105338118 (2022). [https://doi.org/10.1073/pnas.2105338118 <nowiki>[DOI link]</nowiki>]
Title: Destabilization of transverse waves by periodic shear flows


Periodic shear flows have the peculiar property that they are unstable to large-scale, transverse perturbations, and that this instability proceeds via a negative-eddy-viscosity mechanism (Dubrulle & Frisch, 1991). In this talk, I will show an example where this property causes transverse waves to become linearly unstable: a sinusoidal shear flow in the presence of a uniform, streamwise magnetic field in the framework of incompressible MHD. This flow is unstable to a KH-like instability for sufficiently weak magnetic fields, and uniform magnetic fields permit transverse waves known as Alfvén waves. Under the right conditions, these Alfvén waves become unstable, presenting a separate branch of instability that persists for arbitrarily strong magnetic fields which otherwise suppress the KH-like instability. After characterizing these waves with the help of a simple asymptotic expansion, I will show that they drive soliton-like waves in nonlinear simulations. With time permitting, I will discuss other fluid systems where similar dynamics are or may be found, including stratified flows and plasma drift waves.


==== Scott Weady (Flatiron Institute) ====
<div id="Luedtke">
====Jim Luedtke (UW)====
Title: Using integer programming for verification of binarized neural networks


Title: Entropy methods in active suspensions
Binarized neural networks (BNNs) are neural networks in which the weights are binary and the activation functions are the sign function. Verification of BNNs against input perturbation is one way to measure robustness of BNNs. BNN verification can be formulated as an integer linear optimization problem and hence can in theory be solved by state-of-the art methods for integer programming such as the branch-and-cut algorithm implemented in solvers like Gurobi. Unfortunately, the natural formulation is often difficult to solve in practice, even by the best such solvers, due to large integrality gap induced by its so-called "big-M" constraints. We present simple but effective techniques for improving the ability of the integer programming approach to solve the verification problem for BNNs. Along the way, we hope to illustrate more generally some of the strategies integer programmers use to attack difficult problems like this. We find that our techniques enable verifying BNNs against a higher range of input perturbation than using the natural formulation directly.


Collections of active particles, such as suspensions of E. coli or mixtures of microtubules and molecular motors, can exhibit rich non-equilibrium dynamics due to a combination of activity, hydrodynamic interactions, and steric stresses. Continuum kinetic theories, which characterize the set of particle configurations through a continuous distribution function, provide a powerful framework for analyzing such systems and connecting their micro- to macroscopic dynamics. The probabilistic formulation of kinetic theories leads naturally to a characterization in terms of entropy, whether thermodynamic or information-theoretic. In equilibrium systems, entropy strictly increases and always tends towards steady state. This no longer holds in active systems, however entropy still has a convenient mathematical structure. In this talk, we use entropy methods, specifically variational principles involving the relative entropy functional, to study the nonlinear dynamics and stability of active suspensions in the context of the Doi-Saintillan-Shelley kinetic theory. We first present a class of moment closures that arise as constrained minimizers of the relative entropy, and show these closures preserve the kinetic theory's stability and entropic structure while admitting efficient numerical simulation. We then derive variational bounds on relative entropy fluctuations for apolar active suspensions that are closely related to the moment closures. These bounds provide conditions for global stability and yield estimates of time-averaged order parameters. Finally, we discuss applications of these methods to polar active suspensions.
This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.


<div id="Zhdankin">
====Vladimir Zhdankin (UW)====
Title: Exploring astrophysical plasma turbulence with particle-in-cell methods


==== David Saintillan (UC San Diego) ====
Plasmas throughout the universe (as well as in the laboratory) tend to exist in turbulent, nonequilibrium states due to their "collisionless" nature. Described by the Vlasov-Maxwell equations in a six-dimensional phase space (of position and momentum), the basic physics of such plasmas is difficult to model from first principles. There remain open questions about entropy production, nonthermal particle acceleration, energy partition amongst different particle species, and more. Particle-in-cell simulations are a numerical tool that allow us to explore in depth the rich dynamics and statistical mechanics of collisionless plasmas, validating analytical speculation. I will describe some of the results from my group's work on this topic.


Title: Hydrodynamics of active nematic surfaces


The dynamics of biological surfaces often involves the coupling of internal active processes with in-plane orientational order and hydrodynamic flows. Such active surfaces play a key role in various biological processes, from cytokinesis to tissue morphogenesis. In this talk, I will discuss two approaches for the modeling and simulation of active nematic surfaces. In a first model, we analyze the spontaneous dynamics of a freely-suspended viscous drop with surface nematic activity and its coupling with bulk fluid mechanics. Using a spectral boundary integral solver for Stokes flow coupled with a hydrodynamic evolution equation for the nematic tensor, numerical simulations reveal a complex interplay between the flow inside and outside the drop, the surface transport of the nematic field and surface deformations, giving rise to a sequence of self-organized behaviors and symmetry-breaking phenomena of increasing complexity, consistent with experimental observations. In the second part of the talk, I will present a novel computational approach for the simulation of active nematic fluids confined to Riemannian manifolds. The fluid velocity and nematic order parameter are represented as sections of the complex line bundle of a two-manifold. Using a geometric approach based on the Levi-Civita connection, we introduce a coordinate-free discretization method that preserves the continuous local-to-global theorems in differential geometry. Furthermore, we establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. Advection of the nematic field is formulated based on the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. The proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and topology on the hydrodynamics of active nematic systems, and we illustrate its capabilities by simulating active flows on a range of surfaces of increasing complexity.
<div id="Boffi">
====Nick Boffi (CMU)====
Title: Generative modeling with stochastic interpolants


We introduce a class of generative models that unifies flows and diffusions. These models are built using a continuous-time stochastic process called a stochastic interpolant, which exactly connects two arbitrary probability densities in finite time. We show that the time-dependent density of the stochastic interpolant satisfies both a first-order transport equation and an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint yields deterministic and stochastic generative models built dynamically from an ordinary or stochastic differential equation with an adjustable noise level. To formulate a practical algorithm, we discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. Empirically, we highlight the advantages of our formalism -- and the tradeoffs between deterministic and stochastic sampling -- through numerical examples in image generation, inverse imaging, probabilistic forecasting, and accelerated sampling.


<div id="Cockburn">
====Bernardo Cockburn (Minnesota)====
Title: Transforming stabilization into spaces


'''Rose Cersonsky (UW–Madison)'''
In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.


Title: Data-driven approaches to chemical and materials sciences: the importance of data selection, representation, and interpretability
== Archived semesters ==
 
Like many other fields, there has been a recent and overwhelming wave of machine learning and artificial intelligence methods being employed in the chemical sciences. While these methods have the undoubted ability to drive innovation and capabilities, their application to chemical sciences requires a nuanced understanding of molecular representations and structure-property relationships.
 
In this talk, I will discuss the role of molecular featurization – how we transform atoms and molecules into mathematical signals appropriate for machine-learning thermodynamic quantities – and unsupervised analyses that allow us to easily understand and assess these so-called “featurizations” in the context of complex machine learning tasks. In doing so, I will demonstrate how linear methods – that constitute the simplest, most robust, and most transparent approaches to automatically processing large amounts of data – can be leveraged to understand molecular crystallization and aid in pharmaceutical engineering.
 
All methods discussed are available through the open-source [https://scikit-matter.readthedocs.io scikit-matter] software, an official scikit-learn companion that implement methods born out of the materials and chemistry communities.
 
 
==== Di Qi (Purdue) ====
Title: [[#diqi|Statistical Reduced-Order Models and Random Batch Method for Complex Multiscale Systems]]
 
Abstract: The capability of using imperfect stochastic and statistical reduced-order models to capture key statistical features in multiscale nonlinear dynamical systems is investigated. A systematic framework is proposed using a high-order statistical closure enabling accurate prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. A new efficient ensemble forecast algorithm is developed dealing with the nonlinear multiscale coupling mechanism as a characteristic feature in high-dimensional turbulent systems. To address challenges associated with closely coupled spatio-temporal scales in turbulent states and expensive large ensemble simulation for high-dimensional complex systems, we introduce efficient computational strategies using the so-called random batch method. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the new reduced-order model in various dynamical regimes of the flow field with distinct statistical structures. Finally, the proposed model is applied for a wide range of problems in uncertainty quantification, data assimilation, and control.
 
== Future semesters ==


*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[Applied/ACMS/Fall2024|Fall 2024]]
 
*[[Applied/ACMS/Spring2024|Spring 2024]]
== Archived semesters ==
 
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]

Latest revision as of 16:37, 18 February 2025


Applied and Computational Mathematics Seminar


Spring 2025

Date Speaker Title Host(s)
Jan 31 Thomas Chandler (UW) Fluid–structure interactions in active complex fluids Spagnolie
Feb 7 Adrian Fraser (Colorado) Destabilization of transverse waves by periodic shear flows Spagnolie
Feb 14 Jim Luedtke (UW) Using integer programming for verification of binarized neural networks Spagnolie
Feb 21 Vladimir Zhdankin (UW) Exploring astrophysical plasma turbulence with particle-in-cell methods Spagnolie
Feb 28 Nick Boffi (CMU) Generative modeling with stochastic interpolants Li
Mar 7 Suraj Shankar (Michigan) TBA Spagnolie
Mar 14 Yue Lu (Harvard) [Colloquium] TBA Li
Mar 21 Genia Vogman (LLNL) TBA Li
Mar 28 Spring Break
Apr 4 TBA
Apr 11 Pierre Lermusiaux (MIT) TBA Chen
Apr 18 Jack Xin (UC Irvine) [Colloquium] TBA
Apr 25 Bernardo Cockburn (Minnesota) Transforming stabilization into spaces Stechmann, Fabien
May 2 Sylvia Herbert (UCSD) TBA Chen

Abstracts

Thomas G. J. Chandler (UW)

Title: Fluid-structure interactions in active complex fluids

Fluid anisotropy is central to many biological systems, from rod-like bacteria that self-assemble into dense swarms that function as fluids, to the cell cytoskeleton where the active alignment of stiff biofilaments is crucial to cell division. Nematic liquid crystals provide a powerful model for studying these complex environments. However, large immersed bodies elastically frustrate these fluids, leading to intricate interactions. This frustration can be alleviated through body deformations, at the cost of introducing internal stresses. Additionally, active stresses, arising from particle motility or molecular activity, disrupt nematic order by driving flows. In this presentation, I will demonstrate how complex variables enable analytical solutions to a broad range of problems, offering key insights into the roles of body geometry, anchoring conditions, interaction dynamics, activity-induced flows, and body deformations in many biological settings.

Adrian Fraser (Colorado)

Title: Destabilization of transverse waves by periodic shear flows

Periodic shear flows have the peculiar property that they are unstable to large-scale, transverse perturbations, and that this instability proceeds via a negative-eddy-viscosity mechanism (Dubrulle & Frisch, 1991). In this talk, I will show an example where this property causes transverse waves to become linearly unstable: a sinusoidal shear flow in the presence of a uniform, streamwise magnetic field in the framework of incompressible MHD. This flow is unstable to a KH-like instability for sufficiently weak magnetic fields, and uniform magnetic fields permit transverse waves known as Alfvén waves. Under the right conditions, these Alfvén waves become unstable, presenting a separate branch of instability that persists for arbitrarily strong magnetic fields which otherwise suppress the KH-like instability. After characterizing these waves with the help of a simple asymptotic expansion, I will show that they drive soliton-like waves in nonlinear simulations. With time permitting, I will discuss other fluid systems where similar dynamics are or may be found, including stratified flows and plasma drift waves.

Jim Luedtke (UW)

Title: Using integer programming for verification of binarized neural networks

Binarized neural networks (BNNs) are neural networks in which the weights are binary and the activation functions are the sign function. Verification of BNNs against input perturbation is one way to measure robustness of BNNs. BNN verification can be formulated as an integer linear optimization problem and hence can in theory be solved by state-of-the art methods for integer programming such as the branch-and-cut algorithm implemented in solvers like Gurobi. Unfortunately, the natural formulation is often difficult to solve in practice, even by the best such solvers, due to large integrality gap induced by its so-called "big-M" constraints. We present simple but effective techniques for improving the ability of the integer programming approach to solve the verification problem for BNNs. Along the way, we hope to illustrate more generally some of the strategies integer programmers use to attack difficult problems like this. We find that our techniques enable verifying BNNs against a higher range of input perturbation than using the natural formulation directly.

This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.

Vladimir Zhdankin (UW)

Title: Exploring astrophysical plasma turbulence with particle-in-cell methods

Plasmas throughout the universe (as well as in the laboratory) tend to exist in turbulent, nonequilibrium states due to their "collisionless" nature. Described by the Vlasov-Maxwell equations in a six-dimensional phase space (of position and momentum), the basic physics of such plasmas is difficult to model from first principles. There remain open questions about entropy production, nonthermal particle acceleration, energy partition amongst different particle species, and more. Particle-in-cell simulations are a numerical tool that allow us to explore in depth the rich dynamics and statistical mechanics of collisionless plasmas, validating analytical speculation. I will describe some of the results from my group's work on this topic.


Nick Boffi (CMU)

Title: Generative modeling with stochastic interpolants

We introduce a class of generative models that unifies flows and diffusions. These models are built using a continuous-time stochastic process called a stochastic interpolant, which exactly connects two arbitrary probability densities in finite time. We show that the time-dependent density of the stochastic interpolant satisfies both a first-order transport equation and an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint yields deterministic and stochastic generative models built dynamically from an ordinary or stochastic differential equation with an adjustable noise level. To formulate a practical algorithm, we discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. Empirically, we highlight the advantages of our formalism -- and the tradeoffs between deterministic and stochastic sampling -- through numerical examples in image generation, inverse imaging, probabilistic forecasting, and accelerated sampling.

Bernardo Cockburn (Minnesota)

Title: Transforming stabilization into spaces

In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.

Archived semesters


Return to the Applied Mathematics Group Page

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Applied/ACMS&oldid=28131"