BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Richard Nickl (University of Cambridge)
DTSTART:20211101T143000Z
DTEND:20211101T151000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/1
DESCRIPTION:Title: Bayesian non-linear inversion: progress and challenges\nby Richar
d Nickl (University of Cambridge) as part of BIRS workshop: Statistical As
pects of Non-Linear Inverse Problems\n\n\nAbstract\nSolving non-linear inv
erse problems in a modern `data-science’ framework requires a statistica
l formulation of the measurement and error process. Since seminal work of
Andrew Stuart (2010)\, the Bayesian approach has become a popular computat
ional and inferential tool in this context\, and more recently also a theo
retical understanding of the performance of these methods has been develop
ed. We review recent mathematical progress in this field and formulate ana
lytical properties that may render inverse problems provably `solvable’
by Bayesian algorithms. This leads on to many open problems both in the ar
ea of PDEs and inverse problems and in Bayesian nonparametric statistics\,
and we will describe some of those if time permits.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikko Salo (University of Jyväskylä)
DTSTART:20211101T152000Z
DTEND:20211101T160000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/2
DESCRIPTION:Title: Instability mechanisms in inverse problems\nby Mikko Salo (Univer
sity of Jyväskylä) as part of BIRS workshop: Statistical Aspects of Non-
Linear Inverse Problems\n\n\nAbstract\nMany inverse and imaging problems\,
such as image deblurring or electrical/optical tomography\, are known to
be highly sensitive to noise. In these problems small errors in measuremen
ts may lead to large errors in reconstructions. Such problems are called i
ll-posed or unstable\, as opposed to being well-posed (a notion introduced
by J. Hadamard in 1902). Instability also affects the performance of stat
istical algorithms for solving inverse problems. \n\nThe inherent reason f
or instability is easy to understand in linear inverse problems like image
deblurring. For more complicated nonlinear imaging problems the instabili
ty issue is more delicate. We will discuss a general framework for underst
anding instability in inverse problems based on smoothing/compression prop
erties of the forward map together with estimates for entropy and capacity
numbers in relevant function spaces. The methods apply to various inverse
problems involving general geometries and low regularity coefficients.\n\
nThis talk is based on joint work with Herbert Koch (Bonn) and Angkana Rü
land (Heidelberg).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bamdad Hosseini (California Institute of Technology)
DTSTART:20211101T163000Z
DTEND:20211101T171000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/3
DESCRIPTION:Title: Solving and Learning Nonlinear PDEs with Gaussian Processes\nby B
amdad Hosseini (California Institute of Technology) as part of BIRS worksh
op: Statistical Aspects of Non-Linear Inverse Problems\n\n\nAbstract\nIn t
his talk I present a simple\, rigorous\, and interpretable framework for s
olution of nonlinear PDEs based on the framework of Gaussian Processes. Th
e proposed approach provides a natural generalization of kernel methods to
nonlinear PDEs\; has guaranteed convergence\; and inherits the state-of-t
he-art computational complexity of linear solvers for dense kernel matrice
s. I will outline our approach by focusing on an example nonlinear ellipti
c PDE followed by further numerical examples. \nI will also briefly commen
t on extending our approach to solving inverse problems.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schwab (ETHZ)
DTSTART:20211102T143000Z
DTEND:20211102T151000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/4
DESCRIPTION:Title: Deterministic Algorithms for PDEs with GRF inputs\nby Christoph S
chwab (ETHZ) as part of BIRS workshop: Statistical Aspects of Non-Linear I
nverse Problems\n\n\nAbstract\nJoint work with \nDinh Dung and N. Van Kien
\, Hanoi\, Vietnam.\nJakob Zech\, IWR\, Heidelberg\, Germany.\n\nWe consid
er PDEs with (log-)Gaussian random field (GRF for short) inputs. \nParseva
l frames convert GRF inputs into equivalent\, infinite-parametric determin
istic PDEs.\nWe analyze sparsity of Wiener Polynomial Chaos expansions of
the parametric\, deterministic \nforward solution families and of Bayesian
Inverse Problems with GRF priors.\n\nWe present approximation rate bounds
for novel\, deterministic sampling and quadrature algorithms.\nWe cover h
igh order discretizations of PDEs in the physical (space-time) domain\, an
d are free from the CoD. Achieveable convergence rates are superior to tho
se afforded by MC and QMC sampling.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Kaltenbacher (University of Klagenfurt Austria)
DTSTART:20211102T152000Z
DTEND:20211102T160000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/5
DESCRIPTION:Title: Reduced\, all-at-once\, and variational formulations of inverse probl
ems and their solution\nby Barbara Kaltenbacher (University of Klagenf
urt Austria) as part of BIRS workshop: Statistical Aspects of Non-Linear I
nverse Problems\n\n\nAbstract\nThe conventional way of formulating inverse
problems such as identification of a (possibly infinite dimensional) para
meter\, is via some forward operator\, which is the concatenation of the o
bservation operator with the parameter-to-state-map for the underlying mod
el.\nRecently\, all-at-once formulations have been considered as an altern
ative to this reduced formulation\, avoiding the use of a parameter-to-sta
te map\, which would sometimes lead to too restrictive conditions. Here th
e model and the observation are considered simultaneously as one large sys
tem with the state and the parameter as unknowns.\nA still more general fo
rmulation of inverse problems\, containing both the reduced and the all-at
-once formulation\, but also the well-known and highly versatile so-called
variational approach (not to be mistaken with variational regularization)
as special cases\, is to formulate the inverse problem as a minimization
problem (instead of an equation) for the state and parameter. Regularizati
on can be incorporated via imposing constraints and/or adding regularizati
on terms to the objective. \nIn this talk we will provide some new applic
ation examples of minimization based formulations\, such as impedance tomo
graphy with the complete electrode model. Moreover\, we will consider iter
ative regularization methods resulting from the application of gradient or
Newton type iterations to such minimization based formulations and provid
e convergence results.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youssef Marzouk (Massachusetts Institute of Technology)
DTSTART:20211102T163000Z
DTEND:20211102T171000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/6
DESCRIPTION:by Youssef Marzouk (Massachusetts Institute of Technology) as
part of BIRS workshop: Statistical Aspects of Non-Linear Inverse Problems\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Scheichl (Heidelberg University)
DTSTART:20211103T143000Z
DTEND:20211103T151000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/7
DESCRIPTION:Title: Efficient Sample-Based Inference Algorithms in High Dimensions\nb
y Robert Scheichl (Heidelberg University) as part of BIRS workshop: Statis
tical Aspects of Non-Linear Inverse Problems\n\n\nAbstract\nGeneral multiv
ariate distributions are notoriously difficult to sample from\, particular
ly the high-dimensional posterior distributions in PDE-constrained inverse
problems. In this talk\, I present a sampler for arbitrary continuous mul
tivariate distributions based on low-rank surrogates in the tensor-train (
TT) format\, a methodology for scalable\, high-dimensional function approx
imation from computational physics and chemistry. Building upon cross appr
oximation algorithms in linear algebra\, we construct a TT approximation t
o the target probability density function using only a small number of fun
ction evaluations. For sufficiently smooth distributions\, the storage req
uired for accurate TT approximations is moderate\, scaling linearly with d
imension. In turn\, the structure of the tensor-train surrogate allows sam
pling by an efficient conditional distribution method\, since marginal dis
tributions are computable with linear complexity in dimension. I will also
highlight the link to normalizing flows in machine learning and to transp
ort-based variational inference algorithms for high-dimensional distributi
ons. Finally\, I will mention extensions suitable for more strongly concen
trating posterior distributions using a multi-layered approach: the Deep I
nverse Rosenblatt Transport (DIRT) algorithm proposed by Cui and Dolgov in
a recent preprint. This talk is based on joint work with Karim-Anaya Izqu
ierdo (Bath)\, Tiangang Cui (Monash)\, Sergey Dolgov (Bath) and Colin Fox
(Otago).\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Judith Rousseau (Oxford University)
DTSTART:20211103T152000Z
DTEND:20211103T160000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/8
DESCRIPTION:by Judith Rousseau (Oxford University) as part of BIRS worksho
p: Statistical Aspects of Non-Linear Inverse Problems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Stefanov (Purdue)
DTSTART:20211103T163000Z
DTEND:20211103T171000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/9
DESCRIPTION:by Plamen Stefanov (Purdue) as part of BIRS workshop: Statisti
cal Aspects of Non-Linear Inverse Problems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuli Siltanen (University of Helsinki)
DTSTART:20211104T143000Z
DTEND:20211104T151000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/10
DESCRIPTION:by Samuli Siltanen (University of Helsinki) as part of BIRS wo
rkshop: Statistical Aspects of Non-Linear Inverse Problems\n\nAbstract: TB
A\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni S. Alberti (University of Genoa)
DTSTART:20211104T152000Z
DTEND:20211104T160000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/11
DESCRIPTION:Title: Infinite-dimensional inverse problems with finite measurements\n
by Giovanni S. Alberti (University of Genoa) as part of BIRS workshop: Sta
tistical Aspects of Non-Linear Inverse Problems\n\n\nAbstract\nIn this tal
k I will discuss uniqueness\, stability and reconstruction for infinite-di
mensional nonlinear inverse problems with finite measurements\, under the
a priori assumption that the unknown lies in\, or is well-approximated by\
, a finite-dimensional subspace or submanifold. The methods are based on t
he interplay of applied harmonic analysis\, in particular sampling theory
and compressed sensing\, and the theory of inverse problems for partial di
fferential equations. Several examples\, including the Calderón problem
and scattering\, will be discussed.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Glatt-Holtz (Tulane University)
DTSTART:20211104T163000Z
DTEND:20211104T171000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/12
DESCRIPTION:by Nathan Glatt-Holtz (Tulane University) as part of BIRS work
shop: Statistical Aspects of Non-Linear Inverse Problems\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Bohr (University of Cambridge)
DTSTART:20211105T143000Z
DTEND:20211105T151000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/13
DESCRIPTION:by Jan Bohr (University of Cambridge) as part of BIRS workshop
: Statistical Aspects of Non-Linear Inverse Problems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hanne Kekkonen (Delft University of Technology)
DTSTART:20211105T152000Z
DTEND:20211105T160000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/14
DESCRIPTION:Title: Consistency of Bayesian inference for a parabolic inverse problem\nby Hanne Kekkonen (Delft University of Technology) as part of BIRS work
shop: Statistical Aspects of Non-Linear Inverse Problems\n\n\nAbstract\nIn
this talk I will discuss uniqueness\, stability and reconstruction for in
finite-dimensional nonlinear inverse problems with finite measurements\, u
nder the a priori assumption that the unknown lies in\, or is well-approxi
mated by\, a finite-dimensional subspace or submanifold. The methods are b
ased on the interplay of applied harmonic analysis\, in particular samplin
g theory and compressed sensing\, and the theory of inverse problems for p
artial differential equations. Several examples\, including the Calderón
problem and scattering\, will be discussed.\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Wang (MIT)
DTSTART:20211105T163000Z
DTEND:20211105T171000Z
DTSTAMP:20260422T185556Z
UID:BIRS-21w5009/15
DESCRIPTION:by Sven Wang (MIT) as part of BIRS workshop: Statistical Aspec
ts of Non-Linear Inverse Problems\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BIRS-21w5009/15/
END:VEVENT
END:VCALENDAR