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Researcher profile

Houman Owhadi

Houman Owhadi contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningmath.NANumerical AnalysisComputer Science and Game Theorymath.DSmath.OCMethodologyphysics.data-an

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Published work

6 published item(s)

preprint2026arXiv

Dictionary learning for Kernel EDMD

Studying nonlinear dynamical systems through their state space behavior can be challenging, and one possible alternative is to analyze them via their associated Koopman operator. This turns the nonlinear problem into a linear, infinite-dimensional one. To approximate the operator in finite dimensions, extended dynamic mode decomposition (EDMD) is a commonly used algorithm. It requires a finite list of functionals and a set of snapshots from the system to compute an approximation of the operator and its corresponding spectrum. Instead of choosing the list of functionals directly, it can be implicitly defined via kernels, a method known as kernel extended dynamic mode decomposition (kEDMD). However, one still needs to define the kernel and choose its parameter values. In this paper, we aim to streamline this process by extending dictionary learning for EDMD to kernel learning in kEDMD. By simplifying kEDMD we show how to perform gradient-based optimization over the learnable kernel parameters, and demonstrate that this method leads to useful kernels for the original kEDMD. The focus of our work is a method that takes a weighted list of kernels with randomly initialized values as input and outputs a list of kernels and parameter values suitable for approximating the Koopman operator of the underlying system. We demonstrate that unimportant kernels can be removed from the list by analyzing the weights in the weighted sum. We evaluate the method across several experiments, including the Duffing oscillator and the Kuramoto-Sivashinsky PDE, showcasing the method's different strengths.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks

Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with fully interpretable, user-configurable parameters and modular topology, demand process, and control rules. The simulator advances a directed routing graph in discrete time: demand arrives at the destination, is served from stock or recorded as backlog, and triggers replenishment through the network. The state vector tracks per-node on-hand inventory with outstanding orders, in-transit shipments, and a smoothed demand estimate, so the dynamics close as a Markov chain on a tractable state space whose transition kernel acts linearly on the empirical distribution of the state. The released data reproduces the bullwhip effect at empirically consistent magnitudes, and three conservation laws encoded in the Markov chain serve as verification tools when users extend the simulator. We release datasets at two catalogue scales ($C=50$ and $C=200$) with six scenario sweeps producing 30 additional rollouts and 20 Latin-hypercube perturbations, exhibiting dynamics absent from fixed TSF benchmarks: variance amplification, cascading bottlenecks, regime shifts, and cross-channel coupling through shared macro shocks. Zero-shot evaluation of four foundation models (Chronos, Moirai, TimesFM, Lag-Llama) shows MASE values exceeding public GIFT-Eval references at low-to-moderate horizons, supporting incorporation into existing benchmarks. The same pairing produces forecast confidence bands via Latin-hypercube perturbation of demand-side knobs, forward UQ from parameter uncertainty unavailable on standard TSF datasets, demonstrating that foundation models can serve as fast surrogates for the digital twin's forward UQ. Code (MIT): https://github.com/tuhinsahai/ISOMORPH.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Computational Graph Completion

We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing (from data) a computational graph (or hypergraph) representing dependencies between functions and variables. Nodes represent variables, and edges represent functions. Functions and variables may be known, unknown, or random. Data comes in the form of observations of distinct values of a finite number of subsets of the variables of the graph (satisfying its functional dependencies). The underlying problem combines a regression problem (approximating unknown functions) with a matrix completion problem (recovering unobserved variables in the data). Replacing unknown functions by Gaussian Processes (GPs) and conditioning on observed data provides a simple but efficient approach to completing such graphs. Since this completion process can be reduced to an algorithm, as one solves $\sqrt{2}$ on a pocket calculator without thinking about it, one could, with the automation of the proposed framework, solve a complex CSE problem by drawing a diagram. Compared to traditional kriging, the proposed framework can be used to recover unknown functions with much scarcer data by exploiting interdependencies between multiple functions and variables. The underlying problem could therefore also be interpreted as a generalization of that of solving linear systems of equations to that of approximating unknown variables and functions with noisy, incomplete, and nonlinear dependencies. Numerous examples illustrate the flexibility, scope, efficacy, and robustness of the proposed framework and show how it can be used as a pathway to identifying simple solutions to classical CSE problems (digital twin modeling, dimension reduction, mode decomposition, etc.).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Uncertainty Quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball

There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B) requires a prior, it is generally brittle and posterior estimations can be slow. Although (C) leads to the identification of an optimal prior, its approximation suffers from the curse of dimensionality and the notion of risk is one that is averaged with respect to the distribution of the data. We introduce a 4th kind which is a hybrid between (A), (B), (C), and hypothesis testing. It can be summarized as, after observing a sample $x$, (1) defining a likelihood region through the relative likelihood and (2) playing a minmax game in that region to define optimal estimators and their risk. The resulting method has several desirable properties (a) an optimal prior is identified after measuring the data, and the notion of risk is a posterior one, (b) the determination of the optimal estimate and its risk can be reduced to computing the minimum enclosing ball of the image of the likelihood region under the quantity of interest map (which is fast and not subject to the curse of dimensionality). The method is characterized by a parameter in $ [0,1]$ acting as an assumed lower bound on the rarity of the observed data (the relative likelihood). When that parameter is near $1$, the method produces a posterior distribution concentrated around a maximum likelihood estimate with tight but low confidence UQ estimates. When that parameter is near $0$, the method produces a maximal risk posterior distribution with high confidence UQ estimates. In addition to navigating the accuracy-uncertainty tradeoff, the proposed method addresses the brittleness of Bayesian inference by navigating the robustness-accuracy tradeoff associated with data assimilation.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Competitive Mirror Descent

Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we propose competitive mirror descent (CMD): a general method for solving such problems based on first order information that can be obtained by automatic differentiation. First, by adding Lagrange multipliers, we obtain a simplified constraint set with an associated Bregman potential. At each iteration, we then solve for the Nash equilibrium of a regularized bilinear approximation of the full problem to obtain a direction of movement of the agents. Finally, we obtain the next iterate by following this direction according to the dual geometry induced by the Bregman potential. By using the dual geometry we obtain feasible iterates despite only solving a linear system at each iteration, eliminating the need for projection steps while still accounting for the global nonlinear structure of the constraint set. As a special case we obtain a novel competitive multiplicative weights algorithm for problems on the positive cone.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Kernel Mode Decomposition and programmable/interpretable regression networks

Mode decomposition is a prototypical pattern recognition problem that can be addressed from the (a priori distinct) perspectives of numerical approximation, statistical inference and deep learning. Could its analysis through these combined perspectives be used as a Rosetta stone for deciphering mechanisms at play in deep learning? Motivated by this question we introduce programmable and interpretable regression networks for pattern recognition and address mode decomposition as a prototypical problem. The programming of these networks is achieved by assembling elementary modules decomposing and recomposing kernels and data. These elementary steps are repeated across levels of abstraction and interpreted from the equivalent perspectives of optimal recovery, game theory and Gaussian process regression (GPR). The prototypical mode/kernel decomposition module produces an optimal approximation $(w_1,w_2,\cdots,w_m)$ of an element $(v_1,v_2,\ldots,v_m)$ of a product of Hilbert subspaces of a common Hilbert space from the observation of the sum $v:=v_1+\cdots+v_m$. The prototypical mode/kernel recomposition module performs partial sums of the recovered modes $w_i$ based on the alignment between each recovered mode $w_i$ and the data $v$. We illustrate the proposed framework by programming regression networks approximating the modes $v_i= a_i(t)y_i\big(θ_i(t)\big)$ of a (possibly noisy) signal $\sum_i v_i$ when the amplitudes $a_i$, instantaneous phases $θ_i$ and periodic waveforms $y_i$ may all be unknown and show near machine precision recovery under regularity and separation assumptions on the instantaneous amplitudes $a_i$ and frequencies $\dotθ_i$. The structure of some of these networks share intriguing similarities with convolutional neural networks while being interpretable, programmable and amenable to theoretical analysis.

0 citations0 reviewsNo code linkedOpen access