arXiv subjects

James Koch

Publications and source records attributed to James Koch.

17 recordsLinked to original sources

arXiv2026

Non-Exclusive Notifications for Ride-Hailing at Lyft II: Simulations and Marketplace Analysis

Ride-hailing platforms increasingly face uncertain driver acceptance, which makes traditional one-to-one 'exclusive dispatch (ED)' less efficient: rejections and timeouts force sequential retries and lengthen rider wait times, which in turn creates friction in the marketplace. 'Non-exclusive dispatch (NED)' mitigates this friction by broadcasting a request to multiple drivers in parallel. While NED can reduce latency, it introduces new design challenges -- most notably, how to choose notification sets and how to resolve driver contention (when multiple drivers accept the same ride). In this paper -- the second in a two-part collaboration with Lyft -- we develop a theoretically grounded framework to evaluate the long-run performance and marketplace effects of transitioning from ED to NED. We bridge theory and practice by combining (i) an optimization model that formulates NED as a constrained welfare maximization problem with (ii) large-scale discrete-event simulations on proprietary Lyft traces and (iii) a stylized macroscopic equilibrium model. Across simulation and equilibrium analysis, we find that NED improves key fulfillment metrics relative to ED: it reduces match time (and hence rider reneging) while increasing both the number and the average quality of completed matches. We also quantify the speed--quality trade-off between two common contention resolution rules, 'First-Accept' and 'Best-Accept': First-Accept maximizes speed and throughput, whereas Best-Accept is required to maximize per-match quality. Finally, we show that slightly conservative notification heuristics can improve long-run efficiency by avoiding excessive locking of high-value drivers and preserving future availability.

cs.GT↗

arXiv2026

Non-Exclusive Notifications for Ride-Hailing at Lyft I: Single-Cycle Approximation Algorithms

Ride-hailing platforms increasingly rely on non-exclusive notifications-broadcasting a single request to multiple drivers simultaneously-to mitigate inefficiencies caused by uncertain driver acceptance. In this paper, the first in a two-part collaboration with Lyft, we formally model the 'Notification Set Selection Problem' for a single decision cycle, where the platform determines the optimal subset of drivers to notify for each incoming ride request. We analyze this combinatorial optimization problem under two contention-resolution protocols: 'First Acceptance (FA)', which prioritizes speed by assigning the ride to the first responder, and 'Best Acceptance (BA)', which prioritizes match quality by selecting the highest-valued accepting driver. We show that welfare maximization under both mechanisms is strongly NP-hard, ruling out a Fully Polynomial Time Approximation Scheme (FPTAS). Despite this, we derive several positive algorithmic results. For FA, we present a Polynomial Time Approximation Scheme (PTAS) for the single-rider case and a constant-factor approximation (factor 4) for the general matching setting. We highlight that the FA valuation function can be viewed as a novel discrete choice model with theoretical properties of independent interest. For BA, we prove that the objective is monotone and submodular, admitting a standard $(1 - 1/e)$-approximation. Moreover, using a polynomial-time demand oracle that we design for this problem, we show it is possible to surpass the $(1 - 1/e)$ barrier. Finally, in the special case of homogeneous acceptance probabilities, we show that the BA problem can be solved exactly in polynomial time via a linear programming formulation. We validate the empirical performance our algorithms through numerical experiments on synthetic data and on instances calibrated using real ride-sharing data from Lyft.

cs.DS↗

arXiv2025

First Contact: Data-driven Friction-Stir Process Control

This study validates the use of Neural Lumped Parameter Differential Equations for open-loop setpoint control of the plunge sequence in Friction Stir Processing (FSP). The approach integrates a data-driven framework with classical heat transfer techniques to predict tool temperatures, informing control strategies. By utilizing a trained Neural Lumped Parameter Differential Equation model, we translate theoretical predictions into practical set-point control, facilitating rapid attainment of desired tool temperatures and ensuring consistent thermomechanical states during FSP. This study covers the design, implementation, and experimental validation of our control approach, establishing a foundation for efficient, adaptive FSP operations.

eess.SY↗

arXiv2024

STARS: Sensor-agnostic Transformer Architecture for Remote Sensing

We present a sensor-agnostic spectral transformer as the basis for spectral foundation models. To that end, we introduce a Universal Spectral Representation (USR) that leverages sensor meta-data, such as sensing kernel specifications and sensing wavelengths, to encode spectra obtained from any spectral instrument into a common representation, such that a single model can ingest data from any sensor. Furthermore, we develop a methodology for pre-training such models in a self-supervised manner using a novel random sensor-augmentation and reconstruction pipeline to learn spectral features independent of the sensing paradigm. We demonstrate that our architecture can learn sensor independent spectral features that generalize effectively to sensors not seen during training. This work sets the stage for training foundation models that can both leverage and be effective for the growing diversity of spectral data.

cs.CV↗

arXiv2024

Graph Neural Ordinary Differential Equations for Coarse-Grained Socioeconomic Dynamics

We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic relationships -- in the form of ordinary differential equations -- while preserving critical system behaviors. This approach allows for expedited 'what if' studies and sensitivity analyses, essential for informed policy-making. Our findings, from a case study of Baltimore, MD, indicate that this machine learning-augmented coarse-grained model serves as a powerful instrument for deciphering the complex interactions between social factors, geography, and exogenous stressors, offering a valuable asset for system forecasting and resilience planning.

cs.LG↗

arXiv2024

Data-Driven Invertible Neural Surrogates of Atmospheric Transmission

We present a framework for inferring an atmospheric transmission profile from a spectral scene. This framework leverages a lightweight, physics-based simulator that is automatically tuned - by virtue of autodifferentiation and differentiable programming - to construct a surrogate atmospheric profile to model the observed data. We demonstrate utility of the methodology by (i) performing atmospheric correction, (ii) recasting spectral data between various modalities (e.g. radiance and reflectance at the surface and at the sensor), and (iii) inferring atmospheric transmission profiles, such as absorbing bands and their relative magnitudes.

cs.LG↗

arXiv2024

Learning Neural Differential Algebraic Equations via Operator Splitting

Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such as conservation laws. Here, we present an Operator Splitting (OS) numerical integration scheme for learning unknown components of DAEs from time-series data. In this work, we show that the proposed OS-based time-stepping scheme is suitable for relevant system-theoretic data-driven modeling tasks. Presented examples include (i) the inverse problem of tank-manifold dynamics and (ii) discrepancy modeling of a network of pumps, tanks, and pipes. Our experiments demonstrate the proposed method's robustness to noise and extrapolation ability to (i) learn the behaviors of the system components and their interaction physics and (ii) disambiguate between data trends and mechanistic relationships contained in the system.

cs.LG↗

arXiv2023

Neural Lumped Parameter Differential Equations with Application in Friction-Stir Processing

Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity simulations of the physics of a system. In this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.

cs.LG↗

arXiv2022

Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance

Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities observed in practice have a universal characterization which is determined by the overall gain and loss curves of a given system. The universal behavior of damped-driven systems can be understood from a geometrical description of the energy balance with a minimal number of assumptions. The assumptions on the energy dynamics are as follows: the energy increases monotonically as a function of increasing gain, and the losses become increasingly larger with increasing energy, i.e. there are many routes for dissipation in the system for large input energy. The intersection of the gain and loss curves define an energy balanced solution. By constructing an iterative map between the loss and gain curves, the dynamics can be shown to be homeomorphic to the logistic map, which exhibits a period doubling cascade to chaos. Indeed, the loss and gain curves allow for a geometrical description of the dynamics through a simple Verhulst diagram (cobweb plot). Thus irrespective of the physics and its complexities, this simple geometrical description dictates the universal set of logistic map instabilities that arise in complex damped-driven systems. More broadly, damped-driven systems are a class of non-equilibrium pattern forming systems which have a canonical set of instabilities that are manifest in practice.

nlin.AO↗

arXiv2022

Physics-informed Machine Learning of Parameterized Fundamental Diagrams

Fundamental diagrams describe the relationship between speed, flow, and density for some roadway (or set of roadway) configuration(s). These diagrams typically do not reflect, however, information on how speed-flow relationships change as a function of exogenous variables such as curb configuration, weather or other exogenous, contextual information. In this paper we present a machine learning methodology that respects known engineering constraints and physical laws of roadway flux - those that are captured in fundamental diagrams - and show how this can be used to introduce contextual information into the generation of these diagrams. The modeling task is formulated as a probe vehicle trajectory reconstruction problem with Neural Ordinary Differential Equations (Neural ODEs). With the presented methodology, we extend the fundamental diagram to non-idealized roadway segments with potentially obstructed traffic data. For simulated data, we generalize this relationship by introducing contextual information at the learning stage, i.e. vehicle composition, driver behavior, curb zoning configuration, etc, and show how the speed-flow relationship changes as a function of these exogenous factors independent of roadway design.

cs.LG↗

arXiv2022

Structural Inference of Networked Dynamical Systems with Universal Differential Equations

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). In this work, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods is shown with their application to canonical networked nonlinear coupled oscillators.

math.DS↗

arXiv2021

Data-Driven Surrogates of Rotating Detonation Engine Physics with Neural ODEs and High-Speed Camera Footage

Interacting multi-scale physics present in the Rotating Detonation Engine lead to diverse nonlinear dynamical behavior, including combustion wave mode-locking, modulation, and bifurcations. In this work, surrogate models of the RDE physics, including combustion, injection, and mixing, are sought that can reproduce the observed behavior through their interactions. These surrogate models are constructed and trained within the context of Neural ODEs evolving through the latent representation of the waves: the traveling wave coordinate $\xi = x - ct + a$. Shown is that the multi-scale nature of the physics can be successfully separated and analyzed separately, providing valuable insight into the fundamental physical processes of the RDE.

physics.flu-dyn↗

arXiv2021

Data-Driven Modeling of Nonlinear Traveling Waves

Presented is a data-driven Machine Learning (ML) framework for the identification and modeling of traveling wave spatiotemporal dynamics. The presented framework is based on the steadily-propagating traveling wave ansatz, $u(x,t) = U(\xi=x - ct + a)$. For known evolution equations, this coordinate transformation reduces governing partial differential equations (PDEs) to a set of coupled ordinary differential equations (ODEs) in the traveling wave coordinate $\xi$. Although traveling waves are readily observed in many physical systems, the underlying governing equations may be unknown. For these instances, the traveling wave ODEs can be (i) identified in an interpretable manner through an implementation of sparse regression techniques or (ii) modeled empirically with neural ODEs. Presented are these methods applied to several physical systems that admit traveling waves. Examples include traveling wave fronts, pulses, and wavetrains restricted to one-wave wave propagation in a single spatial dimension.

physics.flu-dyn↗

arXiv2020

Data-driven Modeling of Rotating Detonation Waves

The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of co- and/or counter-rotating coherent traveling shock waves whose nonlinear mode-locking behavior exhibit bifurcations and instabilities which are not well understood. Computational fluid dynamics simulations are ubiquitous in characterizing the dynamics of RDE's reactive, compressible flow. Such simulations are prohibitively expensive when considering multiple engine geometries, different operating conditions, and the long-time dynamics of the mode-locking interactions. Reduced-order models (ROMs) provide a critically enabling simulation framework because they exploit low-rank structure in the data to minimize computational cost and allow for rapid parameterized studies and long-time simulations. However, ROMs are inherently limited by translational invariances manifest by the combustion waves present in RDEs. In this work, we leverage machine learning algorithms to discover moving coordinate frames into which the data is shifted, thus overcoming limitations imposed by the underlying translational invariance of the RDE and allowing for the application of traditional dimensionality reduction techniques. We explore a diverse suite of data-driven ROM strategies for characterizing the complex shock wave dynamics and interactions in the RDE. Specifically, we employ the dynamic mode decomposition and a deep Koopman embedding to give new modeling insights and understanding of combustion wave interactions in RDEs.

math.DS↗

arXiv2020

Modeling Thermodynamic Trends of Rotating Detonation Engines

The formation of a number of co- and counter-rotating coherent combustion wave fronts is the hallmark feature of the Rotating Detonation Engine (RDE). The engineering implications of wave topology are not well understood nor quantified, especially with respect to parametric changes in combustor geometry, propellant chemistry, and injection and mixing schemes. In this article, a modeling framework that relates the time and spacial scales of the RDE to engineering performance metrics is developed and presented. The model is built under assumptions of backpressure-insensitivity and nominally choked gaseous propellant injection. The Euler equations of inviscid, compressible fluid flow in one dimension are adapted to model the combustion wave dynamics along the circumference of an annular-type rotating detonation engine. These adaptations provide the necessary mass and energy input and output channels to shape the traveling wave fronts and decaying tails. The associated unit processes of injection, mixing, combustion, and exhaust are all assigned representative time scales necessary for successful wave propagation. We find that the separation, or lack of, these time scales are responsible for the behavior of the system, including wave co- and counter-propagation and bifurcations between these regimes and wave counts. Furthermore, as there is no imposition of wave topology, the model output is used to estimate the net available mechanical work output and thermodynamic efficiency from the closed trajectories through pressure-volume and temperature-entropy spaces. These metrics are investigated with respect to variation in the characteristic scales for the RDE unit physical processes.

physics.flu-dyn↗

arXiv2020

Multi-scale Physics of Rotating Detonation Engines: Autosolitons and Modulational Instabilities

We develop a theoretical framework that predicts and fully characterizes the diverse experimental observations of the nonlinear, combustion wave propagation in a rotating detonation engine (RDE), including the nucleation and formation of combustion pulses, the soliton-like interactions between these combustion fronts, and the fundamental, underlying Hopf bifurcation to time-periodic modulation of the waves. In this framework, the mode-locked structures are classified as autosolitons, or stably-propagating nonlinear waves where the local physics of nonlinearity, dispersion, gain, and dissipation exactly balance. We find that the global dominant balance physics in the RDE combustion chamber are dissipative and multi-scale in nature, with local fast scale (nano- to microseconds) combustion balances generating the fundamental mode-locked autosoliton state, while slow scale (milliseconds) gain-loss balances determine the instabilities and structure of the total number of autosolitons. In this manner, the global multi-scale balance physics give rise to the stable structures - not exclusively the frontal dynamics prescribed by classical detonation theory. Experimental observations and numerical models of the RDE combustion chamber are in strong qualitative agreement with no parameter tuning. Moreover, numerical continuation (computational bifurcation tracking) of the RDE analog system establishes that a Hopf bifurcation of the steadily propagating pulse train leads to the fundamental instability of the RDE, or time-periodic modulation of the waves. Along branches of Hopf orbits in parameter space exist a continuum of wave-pair interactions that exhibit solitonic interactions of varying strength.

physics.flu-dyn↗

arXiv2019

Mode-Locked Rotating Detonation Waves: Experiments and a Model Equation

Direct observation of a Rotating Detonation Engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave fronts and global gain dynamics. We develop a model of the observed dynamics by recasting the Majda detonation analog as an autowave. The solution fronts become attractors of the engine; i.e., mode-locked rotating detonation waves. We find that detonative energy release competes with dissipation and gain recovery to produce the observed dynamics and a bifurcation structure common to driven-dissipative systems, such as mode-locked lasers.

nlin.PS↗