arXiv subjects

Amirhossein Taghvaei

Publications and source records attributed to Amirhossein Taghvaei.

At least 19 recordsLinked to original sources

arXiv2026

Generative models for simulation based filtering: Formulations and Empirical Comparisons

This letter presents a unified formulation and a controlled numerical comparison of generative-model approaches to the nonlinear filtering problem. Under this formulation the analysis step is realized by a transport of the forecast distribution to the posterior, the approaches differing only in how that transport is selected and learned. We derive three new filters, based on stochastic interpolants, their deterministic flow-matching limit, and Schrödinger bridges realized through forward--backward SDEs. We develop a two-stage tuning procedure that separates the training of the generative model from its online refinement. The resulting methods are compared against the optimal transport filter (OTF), the Knothe--Rosenblatt filter (KRF), the sequential importance resampling (SIR) particle filter and the ensemble Kalman filter (EnKF), in terms of accuracy, computational time, and sensitivity to ensemble size and state dimension. The results indicate that every generative filter resolves multimodal posteriors that the EnKF and SIR do not, that no single generative framework dominates, the preferred method being set by the available online budget and ensemble size, and that the filters differ in the regularity of the particle trajectories they produce.

cs.LG↗

arXiv2026

Error Analysis of Triangular Optimal Transport Maps for Filtering

We present a systematic analysis of estimation errors for a class of optimal transport based algorithms for filtering and data assimilation. Along the way, we extend previous error analyses of Brenier maps to the case of conditional Brenier maps that arise in the context of simulation based inference. We then apply these results in a filtering scenario to analyze the optimal transport filtering algorithm of Al-Jarrah et al. (2024, ICML). An extension of that algorithm along with numerical benchmarks on various non-Gaussian and high-dimensional examples are provided to demonstrate its effectiveness and practical potential.

math.ST↗

arXiv2026

Time-Reversed BSDEs for Accurate Gradient Estimation in Diffusion Models

There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC problem by simulating the diffusion process, evaluating a loss function, and applying stochastic optimization algorithms, with adjoint matching emerging as a state-of-the-art approach. However, the adjoint process used in these methods is not adapted to the forward diffusion filtration, which can lead to unstable or high-variance gradient estimates. In this paper, we revisit gradient estimation in diffusion models through the lens of backward stochastic differential equations (BSDEs). We propose an alternative estimator based on a time-reversed BSDE formulation introduced in our prior work, which produces an adjoint process adapted to the underlying filtration. This adapted structure leads to more stable gradient estimates with potentially lower variance. We analyze the accuracy of the proposed estimator and compare it with adjoint matching. Numerical experiments on fine-tuning toy diffusion models demonstrate improved gradient stability and competitive performance.

math.OC↗

arXiv2026

Conditional Sampling via Wasserstein Autoencoders and Triangular Transport

We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning variables. The key idea is to modify a Wasserstein autoencoder to use a (block-) triangular decoder and impose an appropriate independence assumption on the latent variables. We show that the resulting model gives an autoencoder that can exploit low-dimensional structure while simultaneously the decoder can be used for conditional simulation. We explore various theoretical properties of CWAEs, including their connections to conditional optimal transport (OT) problems. We also present alternative formulations that lead to three architectural variants forming the foundation of our algorithms. We present a series of numerical experiments that demonstrate that our different CWAE variants achieve substantial reductions in approximation error relative to the low-rank ensemble Kalman filter (LREnKF), particularly in problems where the support of the conditional measures is truly low-dimensional.

cs.LG↗

arXiv2026

Causal Optimal Coupling for Gaussian Input-Output Distributional Data

We study the problem of identifying an optimal coupling between input-output distributional data generated by a causal dynamical system. The coupling is required to satisfy prescribed marginal distributions and a causality constraint reflecting the temporal structure of the system. We formulate this problem as a Schr"odinger Bridge, which seeks the coupling closest - in Kullback-Leibler divergence - to a given prior while enforcing both marginal and causality constraints. For the case of Gaussian marginals and general time-dependent quadratic cost functions, we derive a fully tractable characterization of the Sinkhorn iterations that converges to the optimal solution. Beyond its theoretical contribution, the proposed framework provides a principled foundation for applying causal optimal transport methods to system identification from distributional data.

eess.SY↗

arXiv2025

A lasso-alternative to Dijkstra's algorithm for identifying short paths in networks

We revisit the problem of finding the shortest path between two selected vertices of a graph and formulate this as an $\ell_1$-regularized regression -- Least Absolute Shrinkage and Selection Operator (lasso). We draw connections between a numerical implementation of this lasso-formulation, using the so-called LARS algorithm, and a more established algorithm known as the bi-directional Dijkstra. Appealing features of our formulation include the applicability of the Alternating Direction of Multiplier Method (ADMM) to the problem to identify short paths, and a relatively efficient update to topological changes.

math.OC↗

arXiv2025

A convex approach for Markov chain estimation from aggregate data via inverse optimal transport

We address the problem of identifying the dynamical law governing the evolution of a population of indistinguishable particles, when only aggregate distributions at successive times are observed. Assuming a Markovian evolution on a discrete state space, the task reduces to estimating the underlying transition probability matrix from distributional data. We formulate this inverse problem within the framework of entropic optimal transport, as a joint optimization over the transition matrix and the transport plans connecting successive distributions. This formulation results in a convex optimization problem, and we propose an efficient iterative algorithm based on the entropic proximal method. We illustrate the accuracy and convergence of the method in two numerical setups, considering estimation from independent snapshots and estimation from a time series of aggregate observations, respectively.

math.OC↗

arXiv2025

Interacting Particle Systems for Fast Linear Quadratic RL

This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates are greatly accelerated by the interactions between particles. Theory focuses on the linear quadratic stochastic optimal control problem for which a complete and novel theory is presented. Apart from the new algorithm, sample complexity bounds are obtained, and it is shown that the mean square error scales as $1/N$ where $N$ is the number of particles. The theoretical results and algorithms are illustrated with numerical experiments and comparisons with other recent approaches, where the faster convergence of the proposed algorithm is numerically demonstrated.

eess.SY↗

arXiv2025

Nonlinear Filtering with Brenier Optimal Transport Maps

This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a stochastic dynamical system given a history of noisy partial observations. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states, due to the weight degeneracy issue. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step. Unlike SIR particle filters, the OT formulation does not require the analytical form of the likelihood. Moreover, it allows us to harness the approximation power of neural networks to model complex and multi-modal distributions and employ stochastic optimization algorithms to enhance scalability. Extensive numerical experiments are presented that compare the OT method to the SIR particle filter and the ensemble Kalman filter, evaluating the performance in terms of sample efficiency, high-dimensional scalability, and the ability to capture complex and multi-modal distributions.

cs.LG↗

arXiv2025

A Time-Reversal Control Synthesis for Steering the State of Stochastic Systems

This paper presents a novel approach for steering the state of a stochastic control-affine system to a desired target within a finite time horizon. Our method leverages the time-reversal of diffusion processes to construct the required feedback control law. Specifically, the control law is the so-called score function associated with the time-reversal of random state trajectories that are initialized at the target state and are simulated backwards in time. A neural network is trained to approximate the score function, enabling applicability to both linear and nonlinear stochastic systems. Numerical experiments demonstrate the effectiveness of the proposed method across several benchmark examples.

math.OC↗

arXiv2025

Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps

In this paper, we present the amortized optimal transport filter (A-OTF) designed to mitigate the computational burden associated with the real-time training of optimal transport filters (OTFs). OTFs can perform accurate non-Gaussian Bayesian updates in the filtering procedure, but they require training at every time step, which makes them expensive. The proposed A-OTF framework exploits the similarity between OTF maps during an initial/offline training stage in order to reduce the cost of inference during online calculations. More precisely, we use clustering algorithms to select relevant subsets of pre-trained maps whose weighted average is used to compute the A-OTF model akin to a mixture of experts. A series of numerical experiments validate that A-OTF achieves substantial computational savings during online inference while preserving the inherent flexibility and accuracy of OTF.

math.OC↗

arXiv2025

Error Analysis of Sampling Algorithms for Approximating Stochastic Optimal Control

This paper is concerned with the error analysis of two types of sampling algorithms, namely model predictive path integral (MPPI) and an interacting particle system (\IPS) algorithm, that have been proposed in the literature for numerical approximation of the stochastic optimal control. The analysis is presented through the lens of Gibbs variational principle. For an illustrative example of a single-stage stochastic optimal control problem, analytical expressions for approximation error and scaling laws, with respect to the state dimension and sample size, are derived. The analytical results are illustrated with numerical simulations.

eess.SY↗

arXiv2025

Time-reversal solution of BSDEs in stochastic optimal control: a linear quadratic study

This paper addresses the numerical solution of backward stochastic differential equations (BSDEs) arising in stochastic optimal control. Specifically, we investigate two BSDEs: one derived from the Hamilton-Jacobi-Bellman equation and the other from the stochastic maximum principle. For both formulations, we analyze and compare two numerical methods. The first utilizes the least-squares Monte-Carlo (LSMC) approach for approximating conditional expectations, while the second leverages a time-reversal (TR) of diffusion processes. Although both methods extend to nonlinear settings, our focus is on the linear-quadratic case, where analytical solutions provide a benchmark. Numerical results demonstrate the superior accuracy and efficiency of the TR approach across both BSDE representations, highlighting its potential for broader applications in stochastic control.

math.OC↗

arXiv2025

Flow matching for stochastic linear control systems

This paper addresses the problem of steering an initial probability distribution to a target probability distribution through a deterministic or stochastic linear control system. Our proposed approach is inspired by the flow matching methodology, with the difference that we can only affect the flow through the given control channels. The motivation comes from applications such as robotic swarms and stochastic thermodynamics, where agents or particles can only be manipulated through control actions. The feedback control law that achieves the task is characterized as the conditional expectation of the control inputs for the stochastic bridges that respect the given control system dynamics. Explicit forms are derived for special cases, and a numerical procedure is presented to approximate the control law, illustrated with examples.

math.OC↗

arXiv2024

How to implement the Bayes' formula in the age of ML?

This chapter contains a self-contained introduction to the significance of Bayes' formula in the context of nonlinear filtering problems. Both discrete-time and continuous-time settings of the problem are considered in a unified manner. In control theory, the focus on optimization-based solution approaches is stressed together with a discussion of historical developments in this area (from 1960s onwards). The heart of this chapter contains a presentation of a novel optimal transportation formulation for the Bayes formula (developed recently by the first author) and its relationship to some of the prior joint work (feedback particle filter) from the authors. The presentation highlights how optimal transportation theory is leveraged to overcome some of the numerical challenges of implementing Bayes' law by enabling the use of machine learning (ML) tools.

eess.SY↗

arXiv2024

Dual Ensemble Kalman Filter for Stochastic Optimal Control

In this paper, stochastic optimal control problems in continuous time and space are considered. In recent years, such problems have received renewed attention from the lens of reinforcement learning (RL) which is also one of our motivation. The main contribution is a simulation-based algorithm -- dual ensemble Kalman filter (EnKF) -- to numerically approximate the solution of these problems. The paper extends our previous work where the dual EnKF was applied in deterministic settings of the problem. The theoretical results and algorithms are illustrated with numerical experiments.

eess.SY↗

arXiv2024

Divergence metrics in the study of Markov and hidden Markov processes

This paper is divided into two parts. The first part reviews the formulae for f-divergences in the study of continuous-time Markov processes and explores their applications in areas such as stochastic stability, the second law of thermodynamics, and its non-equilibrium extensions. This sets the foundation for the second part, which focuses on f-divergence in the study of hidden Markov processes. In this context, we present analyses of filter stability and stochastic thermodynamics, with the latter being used to illustrate the concept of a Maxwell demon in an over-damped Langevin model with white noise observations. The paper's expository style and unified formalism for both Markov and hidden Markov processes aim to serve as a valuable resource for researchers working across related fields.

math.PR↗

arXiv2024

Data-Driven Approximation of Stationary Nonlinear Filters with Optimal Transport Maps

The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a data-driven nonlinear filtering algorithm for the case when the state and observation processes are stationary. The posterior is approximated as the push-forward of an optimal transport (OT) map from a given distribution, that is easy to sample from, to the posterior conditioned on a truncated observation window. The OT map is obtained as the solution to a stochastic optimization problem that is solved offline using recorded trajectory data from the state and observations. An error analysis of the algorithm is presented under the stationarity and filter stability assumptions, which decomposes the error into two parts related to the truncation window during training and the error due to the optimization procedure. The performance of the proposed method, referred to as optimal transport data-driven filter (OT-DDF), is evaluated for several numerical examples, highlighting its significant computational efficiency during the online stage while maintaining the flexibility and accuracy of OT methods in nonlinear filtering.

math.OC↗