arXiv subjects

Floris van Breugel

Publications and source records attributed to Floris van Breugel.

10 recordsLinked to original sources

arXiv2025

A Taxonomy of Numerical Differentiation Methods

Differentiation is a cornerstone of computing and data analysis in every discipline of science and engineering. Indeed, most fundamental physics laws are expressed as relationships between derivatives in space and time. However, derivatives are rarely directly measurable and must instead be computed, often from noisy, potentially corrupt data streams. There is a rich and broad literature of computational differentiation algorithms, but many impose extra constraints to work correctly, e.g. periodic boundary conditions, or are compromised in the presence of noise and corruption. It can therefore be challenging to select the method best-suited to any particular problem. Here we review a broad range of numerical methods for calculating derivatives, present important contextual considerations and choice points, compare relative advantages, and provide basic theory for each algorithm in order to assist users with the mathematical underpinnings. This serves as a practical guide to help scientists and engineers match methods to application domains. We also provide an open-source Python package, PyNumDiff, which contains a broad suite of methods for differentiating noisy data.

math.NA↗

arXiv2025

Discovering and exploiting active sensing motifs for estimation

From organisms to machines, autonomous systems rely on measured sensory cues to estimate unknown information about themselves or their environment. For nonlinear systems, strategic sensor motion can be leveraged to extract otherwise inaccessible information. This principle, known as active sensing, is widespread in biology yet difficult to study, and remains underutilized in engineered systems due to the challenge of systematically designing active sensing motifs. Here, we introduce the method ``BOUNDS: Bounding Observability for Uncertain Nonlinear Dynamic Systems", and Python package pybounds, which can discover movement motifs that increase the information encoded in sensory cues. To exploit sporadic estimates from bouts of active sensing, we further introduce the Augmented Information Kalman Filter (AI-KF). The AI-KF uses insight from BOUNDS to dynamically fuse neural network and model-based estimation. We demonstrate BOUNDS and the AI-KF on a flying agent model and experimental GPS-denied data from a quadcopter, revealing how specific active movements improve estimates of ground speed, altitude, and wind direction. Altogether, our work will prove useful for designing sensor-minimal autonomous systems and investigating active sensing in living organisms.

eess.SY↗

arXiv2025

COSMOS: A Data-Driven Probabilistic Time Series simulator for Chemical Plumes across Spatial Scales

The development of robust odor navigation strategies for automated environmental monitoring applications requires realistic simulations of odor time series for agents moving across large spatial scales. Traditional approaches that rely on computational fluid dynamics (CFD) methods can capture the spatiotemporal dynamics of odor plumes, but are impractical for large-scale simulations due to their computational expense. On the other hand, puff-based simulations, although computationally tractable for large scales and capable of capturing the stochastic nature of plumes, fail to reproduce naturalistic odor statistics. Here, we present COSMOS (Configurable Odor Simulation Model over Scalable Spaces), a data-driven probabilistic framework that synthesizes realistic odor time series from spatial and temporal features of real datasets. COSMOS generates similar distributions of key statistical features such as whiff frequency, duration, and concentration as observed in real data, while dramatically reducing computational overhead. By reproducing critical statistical properties across a variety of flow regimes and scales, COSMOS enables the development and evaluation of agent-based navigation strategies with naturalistic odor experiences. To demonstrate its utility, we compare odor-tracking agents exposed to CFD-generated plumes versus COSMOS simulations, showing that both their odor experiences and resulting behaviors are quite similar.

stat.AP↗

arXiv2025

Duality of Stochastic Observability and Constructability and Links to Fisher Information

Given a set of measurements, observability characterizes the distinguishability of a system's initial state, whereas constructability focuses on the final state in a trajectory. In the presence of process and/or measurement noise, the Fisher information matrices with respect to the initial and final states$\unicode{x2013}$equivalent to the stochastic observability and constructability Gramians$\unicode{x2013}$bound the performance of corresponding estimators through the Cramér-Rao inequality. This letter establishes a connection between stochastic observability and constructability of discrete-time linear systems and provides a more numerically robust way for calculating the stochastic observability Gramian. We define a dual system and show that the dual system's stochastic constructability is equivalent to the original system's stochastic observability, and vice versa. This duality enables the interchange of theorems and tools for observability and constructability. For example, we use this result to translate an existing recursive formula for the stochastic constructability Gramian into a formula for recursively calculating the stochastic observability Gramian for both time-varying and time-invariant systems, where this sequence converges for the latter. Finally, we illustrate the robustness of our formula compared to existing (non-recursive) formulas through a numerical example.

eess.SY↗

arXiv2023

Empirical Individual State Observability

A dynamical system is observable if there is a one-to-one mapping from the system's measured outputs and inputs to all of the system's states. Analytical and empirical tools exist for quantifying the (full state) observability of linear and nonlinear systems; however, empirical tools for evaluating the observability of individual state variables are lacking. Here, a new empirical approach termed Empirical Individual State Observability (E-ISO) is developed to quantify the level of observability of individual state variables. E-ISO first builds an empirical observability matrix via simulation, then applies convex optimization to efficiently determine the subset of its rows required to estimate each state variable individually. Finally, (un)observability measures for these subsets are calculated to provide independent estimates of the observability of each state variable. Multiple example applications of E-ISO on linear and nonlinear systems are shown to be consistent with analytical results. Broadly, E-ISO will be an invaluable tool both for designing active sensing control laws or optimizing sensor placement to increase the observability of individual state variables for engineered systems, and analyzing the trajectory decisions made by organisms.

eess.SY↗

arXiv2023

A Method for Classifying Snow Using Ski-Mounted Strain Sensors

Understanding the structure, quantity, and type of snow in mountain landscapes is crucial for assessing avalanche safety, interpreting satellite imagery, building accurate hydrology models, and choosing the right pair of skis for your weekend trip. Currently, such characteristics of snowpack are measured using a combination of remote satellite imagery, weather stations, and laborious point measurements and descriptions provided by local forecasters, guides, and backcountry users. Here, we explore how characteristics of the top layer of snowpack could be estimated while skiing using strain sensors mounted to the top surface of an alpine ski. We show that with two strain gauges and an inertial measurement unit it is feasible to correctly assign one of three qualitative labels (powder, slushy, or icy/groomed snow) to each 10 second segment of a trajectory with 97% accuracy, independent of skiing style. Our algorithm uses a combination of a data-driven linear model of the ski-snow interaction, dimensionality reduction, and a Naive Bayes classifier. Comparisons of classifier performance between strain gauges suggest that the optimal placement of strain gauges is halfway between the binding and the tip/tail of the ski, in the cambered section just before the point where the unweighted ski would touch the snow surface. The ability to classify snow, potentially in real-time, using skis opens the door to applications that range from citizen science efforts to map snow surface characteristics in the backcountry, and develop skis with automated stiffness tuning based on the snow type.

physics.geo-ph↗

arXiv2021

Emergent behavior and neural dynamics in artificial agents tracking turbulent plumes

Tracking a turbulent plume to locate its source is a complex control problem because it requires multi-sensory integration and must be robust to intermittent odors, changing wind direction, and variable plume statistics. This task is routinely performed by flying insects, often over long distances, in pursuit of food or mates. Several aspects of this remarkable behavior have been studied in detail in many experimental studies. Here, we take a complementary in silico approach, using artificial agents trained with reinforcement learning to develop an integrated understanding of the behaviors and neural computations that support plume tracking. Specifically, we use deep reinforcement learning (DRL) to train recurrent neural network (RNN) agents to locate the source of simulated turbulent plumes. Interestingly, the agents' emergent behaviors resemble those of flying insects, and the RNNs learn to represent task-relevant variables, such as head direction and time since last odor encounter. Our analyses suggest an intriguing experimentally testable hypothesis for tracking plumes in changing wind direction -- that agents follow local plume shape rather than the current wind direction. While reflexive short-memory behaviors are sufficient for tracking plumes in constant wind, longer timescales of memory are essential for tracking plumes that switch direction. At the level of neural dynamics, the RNNs' population activity is low-dimensional and organized into distinct dynamical structures, with some correspondence to behavioral modules. Our in silico approach provides key intuitions for turbulent plume tracking strategies and motivates future targeted experimental and theoretical developments.

q-bio.NC↗

arXiv2021

A Nonlinear Observability Analysis of Ambient Wind Estimation with Uncalibrated Sensors, Inspired by Insect Neural Encoding

Estimating the direction of ambient fluid flow is key for many flying or swimming animals and robots, but can only be accomplished through indirect measurements and active control. Recent work with tethered flying insects indicates that their sensory representation of orientation, apparent flow, direction of movement, and control is represented by a 2-dimensional angular encoding in the central brain. This representation simplifies sensory integration by projecting the direction (but not scale) of measurements with different units onto a universal polar coordinate frame. To align these angular measurements with one another and the motor system does, however, require a calibration of angular gain and offset for each sensor. This calibration could change with time due to changes in the environment or physical structure. The circumstances under which small robots and animals with angular sensors and changing calibrations could self-calibrate and estimate the direction of ambient fluid flow while moving remains an open question. Here, a methodical nonlinear observability analysis is presented to address this. The analysis shows that it is mathematically feasible to continuously estimate flow direction and perform regular self-calibrations by adopting frequent changes in course (or active prevention thereof) and orientation, and requires fusion and temporal differentiation of three sensory measurements: apparent flow, orientation (or its derivative), and direction of motion (or its derivative). These conclusions are consistent with the zigzagging trajectories exhibited by many plume tracking organisms, suggesting that perhaps flow estimation is a secondary driver of their trajectory structure.

eess.SY↗

arXiv2020

Numerical differentiation of noisy data: A unifying multi-objective optimization framework

Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or designing control. Unfortunately, the mathematical formulation of numerical differentiation is typically ill-posed, and researchers often resort to an \textit{ad hoc} process for choosing one of many computational methods and its parameters. In this work, we take a principled approach and propose a multi-objective optimization framework for choosing parameters that minimize a loss function to balance the faithfulness and smoothness of the derivative estimate. Our framework has three significant advantages. First, the task of selecting multiple parameters is reduced to choosing a single hyper-parameter. Second, where ground-truth data is unknown, we provide a heuristic for automatically selecting this hyper-parameter based on the power spectrum and temporal resolution of the data. Third, the optimal value of the hyper-parameter is consistent across different differentiation methods, thus our approach unifies vastly different numerical differentiation methods and facilitates unbiased comparison of their results. Finally, we provide an extensive open-source Python library \texttt{pynumdiff} to facilitate easy application to diverse datasets (https://github.com/florisvb/PyNumDiff).

math.DS↗

arXiv2020

FLIVVER: Fly Lobula Inspired Visual Velocity Estimation & Ranging

The mechanism by which a tiny insect or insect-sized robot could estimate its absolute velocity and distance to nearby objects remains unknown. However, this ability is critical for behaviors that require estimating wind direction during flight, such as odor-plume tracking. Neuroscience and behavior studies with insects have shown that they rely on the perception of image motion, or optic flow, to estimate relative motion, equivalent to a ratio of their velocity and distance to objects in the world. The key open challenge is therefore to decouple these two states from a single measurement of their ratio. Although modern SLAM (Simultaneous Localization and Mapping) methods provide a solution to this problem for robotic systems, these methods typically rely on computations that insects likely cannot perform, such as simultaneously tracking multiple individual visual features, remembering a 3D map of the world, and solving nonlinear optimization problems using iterative algorithms. Here we present a novel algorithm, FLIVVER, which combines the geometry of dynamic forward motion with inspiration from insect visual processing to \textit{directly} estimate absolute ground velocity from a combination of optic flow and acceleration information. Our algorithm provides a clear hypothesis for how insects might estimate absolute velocity, and also provides a theoretical framework for designing fast analog circuitry for efficient state estimation, which could be applied to insect-sized robots.

cs.RO↗