arXiv subjects

Arunava Banerjee

Publications and source records attributed to Arunava Banerjee.

18 recordsLinked to original sources

arXiv2026

Data-driven design of steady-state feedforward inputs for nonlinear systems under partial measurement

Designing trajectory tracking controllers for nonlinear systems remains a significant challenge, traditionally requiring precise mathematical models and complex analytical derivations. While the Internal Model Principle (IMP) provides a robust theoretical foundation for such problems, its application is often hindered by model uncertainty and the inherent complexity of nonlinear controller synthesis. This work proposes a practical data-driven control framework that bypasses the need for an explicit first-principles model by utilizing raw input-output data. By integrating fundamental results from IMP theory with nonlinear system analysis, the proposed approach improves design tractability. The framework's efficacy is validated through numerical simulations on two distinct nonlinear platforms: a mechanical load with a nonlinear friction term and an electrohydraulic actuator system.

eess.SY↗

arXiv2026

Certified Feedforward Tracking for Unknown Nonlinear Systems via Invertible Neural Networks

In this paper, we address the certification of datadriven feedforward control for periodic tracking of unknown nonlinear systems under partial state measurements. To this end, we adopt an invertible neural network (INN) as a surrogate for the unknown system. This choice allows us to bypass solving a nonconvex inversion problem, eliminating the associated inversion errors and reducing tracking error certification to a surrogate modeling problem. We then apply conformal prediction to provide finite-sample probabilistic guarantees on the surrogate modeling error which, through the derived tracking error bound, yield marginal certificates on feedforward tracking error. Finally, we demonstrate the approach on a DC-motor-driven mechanical load with nonlinear friction.

eess.SY↗

arXiv2026

Learning-Based Decision Making for Combustion Phasing Control in Multi-Fuel CI Engines with Latent Fuel Reactivity Estimation

Multi-fuel compression-ignition engines offer fuel flexibility but introduce uncertain, time-varying fuel reactivity, represented by cetane number (CN), which complicates cycle-to-cycle combustion-phasing control. This work formulates CA50 regulation under latent CN variation as a partially observable sequential decision problem and systematically evaluates controllers with increasing temporal and representational capacity, including LinUCB, history-augmented contextual bandits, observation-only DDPG, recurrent DDPG, and a proposed GRU-guided RL framework. A Gaussian-process surrogate trained on experimental multi-fuel engine data provides a controlled and reproducible evaluation environment. Results show that myopic and fixed-history bandit methods degrade under CN variation, observation-only RL suffers from latent-state aliasing, and generic recurrence is insufficient when CN evolves rapidly. The proposed framework learns a compact GRU-based representation of fuel reactivity from combustion history and conditions both actor and critic on this estimated signal rather than oracle CN. By training the policy on the same imperfect fuel-reactivity information available at deployment, the controller avoids train-deploy inconsistency in conventional online estimate-then-control pipelines. Across unseen CN trajectories, the policy achieves stable CA50 regulation with mean absolute tracking error below 0.25{\deg} CA at the training setpoint, while producing smooth, physically consistent SOI and glow-plug-power actuation. These results show that combustion control under latent, continuously evolving fuel dynamics requires more than standalone estimation or generic recurrence. By aligning fuel-reactivity inference with control policy learning, the proposed framework enables reactivity-aware decision-making using the same estimated state available during deployment.

eess.SY↗

arXiv2026

Data-driven Control with Real-time Uncertainty Compensation for Multi-Fuel Engines

Multi-fuel compression ignition (CI) engines offer superior power density and fuel flexibility. However, achieving consistent and optimal combustion phasing across a wide range of operating conditions remains a major challenge, particularly in the presence of modeling uncertainties. This paper presents a novel, data-driven real-time uncertainty compensation framework for combustion control in multi-fuel CI engines. The proposed approach introduces a pseudo-engine speed that enables dynamic adaptation of control inputs in response to uncertainty affecting the engine. To model the underlying combustion process, a Gaussian Process Regression (GPR) model is first trained on available input-output data, capturing the nonlinear and fuel-dependent behavior across varying operating conditions. Control inputs are then synthesized through model inversion of the learned GPR surrogate and augmented with an uncertainty compensator designed to mitigate deviations caused by dynamic variations in operating conditions and model inaccuracies. This integrated control strategy allows for real-time input corrections within a finite number of combustion cycles. Theoretical analysis establishes finite-time convergence guarantees for the proposed controller. Simulation results demonstrate that the proposed method steers the combustion phasing to the desired value in real-time, providing a scalable and adaptive control solution for multi-fuel CI engine operation.

eess.SY↗

arXiv2025

Global Asymptotic Rates Under Randomization: Gauss-Seidel and Kaczmarz

Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap, leveraging a new technique for bounding the spectral radii of operators arising in randomized iterations and a connection we establish to Perron-Frobenius theory for noncommutative algebras. The asymptotic analysis also uncovers and quantifies the previously unexplained role of relaxation in improving performance, thereby resolving an open problem posed by Strohmer and Vershynin in 2007.

math.NA↗

arXiv2024

Robust online reconstruction of continuous-time signals from a lean spike train ensemble code

Sensory stimuli in animals are encoded into spike trains by neurons, offering advantages such as sparsity, energy efficiency, and high temporal resolution. This paper presents a signal processing framework that deterministically encodes continuous-time signals into biologically feasible spike trains, and addresses the questions about representable signal classes and reconstruction bounds. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons using a convolve-then-threshold mechanism with various convolution kernels. A closed-form solution to the inverse problem, from spike trains to signal reconstruction, is derived in the Hilbert space of shifted kernel functions, ensuring sparse representation of a generalized Finite Rate of Innovation (FRI) class of signals. Additionally, inspired by real-time processing in biological systems, an efficient iterative version of the optimal reconstruction is formulated that considers only a finite window of past spikes, ensuring robustness of the technique to ill-conditioned encoding; convergence guarantees of the windowed reconstruction to the optimal solution are then provided. Experiments on a large audio dataset demonstrate excellent reconstruction accuracy at spike rates as low as one-fifth of the Nyquist rate, while showing clear competitive advantage in comparison to state-of-the-art sparse coding techniques in the low spike rate regime.

cs.NE↗

arXiv2024

Gaussian Recombining Split Tree

Binomial trees are widely used in the financial sector for valuing securities with early exercise characteristics, such as American stock options. However, while effective in many scenarios, pricing options with CRR binomial trees are limited. Major limitations are volatility estimation, constant volatility assumption, subjectivity in parameter choices, and impracticality of instantaneous delta hedging. This paper presents a novel tree: Gaussian Recombining Split Tree (GRST), which is recombining and does not need log-normality or normality market assumption. GRST generates a discrete probability mass function of market data distribution, which approximates a Gaussian distribution with known parameters at any chosen time interval. GRST Mixture builds upon the GRST concept while being flexible to fit a large class of market distributions and when given a 1-D time series data and moments of distributions at each time interval, fits a Gaussian mixture with the same mixture component probabilities applied at each time interval. Gaussian Recombining Split Tre Mixture comprises several GRST tied using Gaussian mixture component probabilities at the first node. Our extensive empirical analysis shows that the option prices from the GRST align closely with the market.

q-fin.CP↗

arXiv2021

Kaczmarz and Gauss-Seidel Algorithms with Volume Sampling

The method of Alternating Projections (AP) is a fundamental iterative technique with applications to problems in machine learning, optimization and signal processing. Examples include the Gauss-Seidel algorithm which is used to solve large-scale regression problems and the Kaczmarz and projections onto convex sets (POCS) algorithms that are fundamental to iterative reconstruction. Progress has been made with regards to the questions of efficiency and rate of convergence in the randomized setting of the AP method. Here, we extend these results with volume sampling to block (batch) sizes greater than 1 and provide explicit formulas that relate the convergence rate bounds to the spectrum of the underlying system. These results, together with a trace formula and associated volume sampling, prove that convergence rates monotonically improve with larger block sizes, a feature that can not be guaranteed in general with uniform sampling (e.g., in SGD).

math.NA↗

arXiv2020

Spike-Triggered Descent

The characterization of neural responses to sensory stimuli is a central problem in neuroscience. Spike-triggered average (STA), an influential technique, has been used to extract optimal linear kernels in a variety of animal subjects. However, when the model assumptions are not met, it can lead to misleading and imprecise results. We introduce a technique, called spike-triggered descent (STD), which can be used alone or in conjunction with STA to increase precision and yield success in scenarios where STA fails. STD works by simulating a model neuron that learns to reproduce the observed spike train. Learning is achieved via parameter optimization that relies on a metric induced on the space of spike trains modeled as a novel inner product space. This technique can precisely learn higher order kernels using limited data. Kernels extracted from a Locusta migratoria tympanal nerve dataset demonstrate the strength of this approach.

q-bio.NC↗

arXiv2019

A Bayesian Approach for Analyzing Data on the Stiefel Manifold

Directional data emerges in a wide array of applications, ranging from atmospheric sciences to medical imaging. Modeling such data, however, poses unique challenges by virtue of their being constrained to non-Euclidean spaces like manifolds. Here, we present a unified Bayesian framework for inference on the Stiefel manifold using the Matrix Langevin distribution. Specifically, we propose a novel family of conjugate priors and establish a number of theoretical properties relevant to statistical inference. %Importantly, these include the propriety of these priors and concentration characterization. Conjugacy enables the translation of these properties to their corresponding posteriors, which we exploit to develop the posterior inference scheme. For the implementation of the posterior computation, including the posterior sampling, we adopt a novel computational procedure for evaluating the hypergeometric function of matrix arguments that appears as normalization constants in the relevant densities.

math.ST↗

arXiv2019

Signal Coding and Perfect Reconstruction using Spike Trains

In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of the spiking neuron, is presented. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons via a standard convolve-then-threshold mechanism. Neurons are distinguished by their convolution kernels and threshold values. Reconstruction is posited as a convex optimization minimizing energy. Formal conditions under which perfect reconstruction of the signal from the spike trains is possible are then identified in this setup. Finally, a stochastic gradient descent mechanism is proposed to achieve these conditions. Simulation experiments are presented to demonstrate the strength and efficacy of the framework

q-bio.NC↗

arXiv2018

Multi-Scale Generalized Plane Match for Optical Flow

Despite recent advances, estimating optical flow remains a challenging problem in the presence of illumination change, large occlusions or fast movement. In this paper, we propose a novel optical flow estimation framework which can provide accurate dense correspondence and occlusion localization through a multi-scale generalized plane matching approach. In our method, we regard the scene as a collection of planes at multiple scales, and for each such plane, compensate motion in consensus to improve match quality. We estimate the square patch plane distortion using a robust plane model detection method and iteratively apply a plane matching scheme within a multi-scale framework. During the flow estimation process, our enhanced plane matching method also clearly localizes the occluded regions. In experiments on MPI-Sintel datasets, our method robustly estimated optical flow from given noisy correspondences, and also revealed the occluded regions accurately. Compared to other state-of-the-art optical flow methods, our method shows accurate occlusion localization, comparable optical flow quality, and better thin object detection.

cs.CV↗

arXiv2017

A Bayesian Mixture Model for Clustering on the Stiefel Manifold

Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on. A general, and novel, family of conjugate priors, and an efficient Markov chain Monte Carlo (MCMC) sampling scheme for the corresponding posteriors is then developed for the mixture model. Theoretical properties of the prior and posterior distributions, including posterior consistency, are explored in detail. Extensive simulation experiments are presented to validate the efficacy of the framework. Real-world examples, including a large scale neuroimaging dataset, are analyzed to demonstrate the computational tractability of the approach.

stat.ME↗

arXiv2017

Learning Feedforward and Recurrent Deterministic Spiking Neuron Network Feedback Controllers

We address the problem of learning feedback control where the controller is a network constructed solely of deterministic spiking neurons. In contrast to previous investigations that were based on a spike rate model of the neuron, the control signal here is determined by the precise temporal positions of spikes generated by the output neurons of the network. We model the problem formally as a hybrid dynamical system comprised of a closed loop between a plant and a spiking neuron network. We derive a novel synaptic weight update rule via which the spiking neuron network controller learns to hold process variables at desired set points. The controller achieves its learning objective based solely on access to the plant's process variables and their derivatives with respect to changing control signals; in particular, it requires no internal model of the plant. We demonstrate the efficacy of the rule by applying it to the classical control problem of the cart-pole (inverted pendulum) and a model of fish locomotion. Experiments show that the proposed controller has a stability region comparable to a traditional PID controller, its trajectories differ qualitatively from those of a PID controller, and in many instances the controller achieves its objective using very sparse spike train outputs.

q-bio.NC↗

arXiv2015

Sensitivity Analysis for additive STDP rule

Spike Timing Dependent Plasticity (STDP) is a Hebbian like synaptic learning rule. The basis of STDP has strong experimental evidences and it depends on precise input and output spike timings. In this paper we show that under biologically plausible spiking regime, slight variability in the spike timing leads to drastically different evolution of synaptic weights when its dynamics are governed by the additive STDP rule.

q-bio.NC↗

arXiv2014

Learning Precise Spike Train to Spike Train Transformations in Multilayer Feedforward Neuronal Networks

We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation to the deterministic spiking neuron setting, is based strictly on spike timing and avoids invoking concepts pertaining to spike rates or probabilistic models of spiking. The derivation is founded on two innovations. First, an error functional is proposed that compares the spike train emitted by the output neuron of the network to the desired spike train by way of their putative impact on a virtual postsynaptic neuron. This formulation sidesteps the need for spike alignment and leads to closed form solutions for all quantities of interest. Second, virtual assignment of weights to spikes rather than synapses enables a perturbation analysis of individual spike times and synaptic weights of the output as well as all intermediate neurons in the network, which yields the gradients of the error functional with respect to the said entities. Learning proceeds via a gradient descent mechanism that leverages these quantities. Simulation experiments demonstrate the efficacy of the proposed learning framework. The experiments also highlight asymmetries between synapses on excitatory and inhibitory neurons.

cs.NE↗

arXiv2014

Connectomic Constraints on Computation in Feedforward Networks of Spiking Neurons

Several efforts are currently underway to decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function of the said circuit is unknown. We consider, here, the question of how the wiring diagram of neurons imposes constraints on what neural circuits can compute, when we cannot assume detailed information on the physiological response properties of the neurons. We call such constraints -- that arise by virtue of the connectome -- connectomic constraints on computation. For feedforward networks equipped with neurons that obey a deterministic spiking neuron model which satisfies a small number of properties, we ask if just by knowing the architecture of a network, we can rule out computations that it could be doing, no matter what response properties each of its neurons may have. We show results of this form, for certain classes of network architectures. On the other hand, we also prove that with the limited set of properties assumed for our model neurons, there are fundamental limits to the constraints imposed by network structure. Thus, our theory suggests that while connectomic constraints might restrict the computational ability of certain classes of network architectures, we may require more elaborate information on the properties of neurons in the network, before we can discern such results for other classes of networks.

q-bio.NC↗

arXiv2011

An application of the stationary phase method for estimating probability densities of function derivatives

We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a uniformly distributed random variable) defined on a closed, bounded interval \Omega \subset R is accurately approximated by the normalized power spectrum of \phi=exp(iS/\tau) as the free parameter \tau-->0. The result is shown using the well known stationary phase approximation and standard integration techniques and requires proper ordering of limits. Experimental results provide anecdotal visual evidence corroborating the result.

stat.ML↗