Filters








269 Hits in 4.4 sec

Riemannian Diffusion Schrödinger Bridge [article]

James Thornton, Michael Hutchinson, Emile Mathieu, Valentin De Bortoli, Yee Whye Teh, Arnaud Doucet
2022 arXiv   pre-print
To overcome these issues, we introduce Riemannian Diffusion Schrödinger Bridge.  ...  Our proposed method generalizes Diffusion Schrödinger Bridge introduced in to the non-Euclidean setting and extends Riemannian score-based models beyond the first time reversal.  ...  Riemannian Diffusion Schrödinger Bridge In Euclidean state spaces, De Bortoli et al. ( 2021 ) proposed Diffusion Schrödinger Bridge (DSB), an algorithm to approximate the solution to the SB problem based  ... 
arXiv:2207.03024v1 fatcat:rdeza3l6ynbyzje7tvqctrgny4

A geometric perspective on regularized optimal transport [article]

Flavien Léger
2017 arXiv   pre-print
We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schr\"odinger bridge problem and the Yasue problem.  ...  Reversing the arrow of time in (SB) leads to the backward-in-time Schrödinger bridge problem (SB*); it amounts to change the sign of the diffusion coefficient γ : (SB*) minimize ρ, b * 1 0 1 2 |b * t (  ...  Forward and backward Schrödinger bridge problems.  ... 
arXiv:1703.10243v2 fatcat:fovp6stnlzaahdglyl42xaslrm

Extremal flows on Wasserstein space [article]

Giovanni Conforti, Michele Pavon
2017 arXiv   pre-print
We show that the flows associated to the Schroedinger bridge with general prior, to Optimal Mass Transport and to the Madelung fluid can all be characterized as annihilating the first variation of a suitable  ...  It is known that the Schrödinger bridge is the law of a diffusion process Q whose generator is of the same form as P , i.e. σ 2 ∆ + c t · ∇, for some time-dependent vector field c t (x).  ...  Section III is devoted to Schrödinger bridges and entropic interpolation.  ... 
arXiv:1712.02257v1 fatcat:5brig7vydfgxjhcmjmoj5t775q

Some geometric ideas for feature enhancement of diffusion tensor fields

Hamza Farooq, Yongxin Chen, Tryphon T. Georgiou, Christophe Lenglet
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  
Diffusion Tensor Tomography generates a 3dimensional 2-tensor field that encapsulates properties of probed matter.  ...  This consensus is amplified along directions where distances in the Riemannian metric are short.  ...  Future Work In analogy to the stochastic framework of Schrödinger bridges [12] - [15] where a path ρ t is constructed to interpolate two end-point in time density functions-a stochastic control problem  ... 
doi:10.1109/cdc.2016.7798851 dblp:conf/cdc/FarooqCGL16 fatcat:mvzjau5tjvb2vcl4jrffcaiq4y

Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [article]

Guillaume Huguet, D.S. Magruder, Oluwadamilola Fasina, Alexander Tong, Manik Kuchroo, Guy Wolf, Smita Krishnaswamy
2022 arXiv   pre-print
We show that this method is superior to normalizing flows, Schr\"odinger bridges and other generative models that are designed to flow from noise to data in terms of interpolating between populations.  ...  For example [9] , solve the Schrödinger bridge (SB) between two distributions.  ...  Examples include score-based generative matching [32, 33] , diffusion models [17] , Schrödinger bridges [26, 9] , and continuous normalizing flows (CNF) [6, 14] .  ... 
arXiv:2206.14928v1 fatcat:cry7jikoyfhltiyeguco3bqpl4

Extensions of Brownian motion to a family of Grushin-type singularities [article]

Ugo Boscain, Robert W. Neel
2019 arXiv   pre-print
on the Riemannian part for these surfaces.  ...  Nonetheless, we again describe a "best" extension which respects the isometry group, and in this case, this diffusion corresponds to the bridging extension.  ...  Moreover, this is the diffusion associated to the bridging extension.  ... 
arXiv:1910.02256v1 fatcat:34yahgmtozdq7m26bpwz4ci4ze

A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost [article]

Giovanni Conforti
2018 arXiv   pre-print
In this article, we prove that the Schrödinger bridge solves a second order equation in the Riemannian structure of optimal transport.  ...  Its optimal value, the entropic transportation cost, and its optimal solution, the Schrödinger bridge, stand as the natural probabilistic counterparts to the transportation cost and displacement interpolation  ...  An equation for the Schrödinger bridge.  ... 
arXiv:1704.04821v4 fatcat:o3bu5hrc3vd5dplxptq4ysoize

Optimal Transport Over a Linear Dynamical System

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
2017 IEEE Transactions on Automatic Control  
In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schrödinger bridge.  ...  The form of solution underscores the connection between the two and that the OMT-wpd is the limit of the Schrödinger bridge problem when the diffusion term vanishes.  ...  This suggests that the minimizer of the OMT-wpd might be obtained as the limit of the joint initial-final time distribution of solutions to the Schrödinger bridge problems as the diffusivity goes to zero  ... 
doi:10.1109/tac.2016.2602103 fatcat:7xra2v2wmbh6vdnuxcllfo77ey

Optimal transport over a linear dynamical system [article]

Yongxin Chen, Tryphon Georgiou, Michele Pavon
2015 arXiv   pre-print
In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schrödinger bridge.  ...  The form of solution underscores the connection between the two and that the OMT-wpd is the limit of the Schrödinger bridge problem when the diffusion term vanishes.  ...  This suggests that the minimizer of the OMT-wpd might be obtained as the limit of the joint initial-final time distribution of solutions to the Schrödinger bridge problems as the diffusivity goes to zero  ... 
arXiv:1502.01265v1 fatcat:ooay2ofdejeh7gubmnwnsfnule

General Relativity and the Ricci Flow [article]

Mohammed Alzain
2022 arXiv   pre-print
In Riemannian geometry, the Ricci flow is the analogue of heat diffusion; a deformation of the metric tensor driven by its Ricci curvature.  ...  In fact, a key ingredient in the time-dependent Schrödinger equation is the background Newtonian time.  ...  manifold to evolve (even in the absence of matter) with respect to an external time variable, hence, the Ricci flow is an essential tool in bridging a major gap between the general theory of relativity  ... 
arXiv:2209.00952v1 fatcat:nskl2evwxja3fmoxpqd4m2yqwa

Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces [article]

Yongxin Chen, Tryphon Georgiou, Michele Pavon
2016 arXiv   pre-print
We then study the evolution of relative entropy in the case of uncontrolled-controlled diffusions.  ...  Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints.  ...  This is then specialized to the Schrödinger bridge. II.  ... 
arXiv:1601.04891v1 fatcat:jw3yx4tgtjaajcxve5cw7ebwyi

On observation of position in quantum theory

A. Kryukov
2018 Journal of Mathematical Physics  
A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered.  ...  Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment.  ...  More importantly, the embedding ω σ = ρ σ •ω of R 3 into the space of states L 2 (R 3 ) together with the vector representation of observables provide us with a bridge between Newtonian to Schrödinger  ... 
doi:10.1063/1.5029350 fatcat:wixivtmlrrer5kxmdgiiktnhcu

Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds

Robert Grummt, Martin Kolb
2012 Journal of Mathematical Analysis and Applications  
In this paper we extend the well-known Leinfelder-Simader theorem on the essential selfadjointness of singular Schrödinger operators to arbitrary complete Riemannian manifolds.  ...  In the last decade there has been a lot of interest in properties of Schrödinger operators on Riemannian manifolds (see e.g. [1, 4, 16, 8, 20] ).  ...  Consider the diffusion operator D := − + grad ln F · ∇ =: − + b · ∇ in the case M = R n .  ... 
doi:10.1016/j.jmaa.2011.09.060 fatcat:s6iorkvaujdmdp7tolb5gptfhi

Construction of self-adjoint Berezin–Toeplitz operators on Kähler manifolds and a probabilistic representation of the associated semigroups

Bernhard G. Bodmann
2003 Journal of Geometry and Physics  
More explicitly, the integration is taken over Brownian-motion paths in phase space in the ultra-diffusive limit.  ...  All results are the consequence of a relation between Berezin-Toeplitz operators and Schrodinger operators defined via certain quadratic forms.  ...  It is derived from a version of the Feynman-Kac formula for Schrödinger operators on Riemannian manifolds.  ... 
doi:10.1016/s0393-0440(02)00191-2 fatcat:jqbwi45cmjfrtgnc4n3qsimfei

Stochastic control liaisons: Richard Sinkhorn meets Gaspard Monge on a Schroedinger bridge [article]

Yongxin Chen, Tryphon T. Georgiou, Michele Pavon
2020 arXiv   pre-print
This so-called Schroedinger bridge problem (SBP) was recently recognized as a regularization of the Monge-Kantorovich Optimal Mass Transport (OMT), leading to effective computation of the latter.  ...  modern science dealing with the so-called Sinkhorn algorithm which appears as a special case of an algorithm first studied by the French analyst Robert Fortet in 1938/40 specifically for Schroedinger bridges  ...  In [58] , a similar approach was taken in the context of diffusion processes leading to a new proof of a classical result of Jamison on existence and uniqueness for the Schrödinger bridge and providing  ... 
arXiv:2005.10963v3 fatcat:qbrb3qebjjhllnoim4n6olxos4
« Previous Showing results 1 — 15 out of 269 results