AIRA-dojo: Automated Time Series Analysis & Control

• AIRA-dojo is a framework that automates impulse response analysis by integrating VAR models with gradient-based optimization for personalized interventions.
• It converts individual time series data into actionable insights using cumulative impulse response functions to rank multivariate influences efficiently.
• The system leverages differentiable physics via platforms like Dojo to validate gradient-based control, ensuring reliable simulation in dynamic robotics and health applications.

AIRA-dojo refers to a set of methodologies and systems rooted in the automation of time series analysis for individualized modeling, prediction, and optimal control, with a particular focus on applications such as personalized well-being interventions and differentiable robotics simulation. The term encompasses the Automated Impulse Response Analysis (AIRA) framework—originally developed for personalized advice from longitudinal mental health data—as well as the application of differentiable physics and control systems as demonstrated in platforms like Dojo and related differentiable simulation tools. Collectively, AIRA-dojo represents the integration of advanced vector autoregressive modeling, impulse response function analysis, and gradient-based optimization within scalable, computationally efficient packages designed to facilitate personalized, data-driven feedback and control.

1. Foundations: Automated Impulse Response Analysis (AIRA)

AIRA is an algorithmic pipeline devised to convert high-frequency, individual-level time series data (e.g., ecological momentary assessment or sensor observations) into actionable advice that supports well-being and self-management. The computational backbone of AIRA comprises two key elements:

• Vector Autoregression (VAR) Models: The VAR($p$) model employed by AIRA is of the form

$$Y_t = c + B^1 Y_{t-1} + B^2 Y_{t-2} + \dots + B^p Y_{t-p} + \xi X + e_t$$

where $Y_t$ is an $m$-dimensional vector of endogenous variables, $X$ comprises exogenous covariates, $B^i$ and $\xi$ are coefficient matrices, and $e_t$ is a residual vector.

• Impulse Response Functions (IRF): AIRA automates the derivation of IRFs by transforming the VAR into its vector moving average (VMA) representation and simulating the effects of exogenous "shocks" to each variable across a specified horizon. For variable $x$, the IRF targeting variable $y$ is computed as

$$\mathrm{irf}(x, y, k) = \left[ (\psi_0 \alpha(x))_y, \dots, (\psi_k \alpha(x))_y \right]^\top$$

with $\psi_0 = I_m$ and

$\psi_i = \sum_{j=1}^i C_{i,j}$

where $C_{i,j}$ are recursively derived VMA coefficients and $\alpha(x)$ is a selector vector. The cumulative impulse response function is then

$$\mathrm{irf_{cum}}(x, y, k) = \sum_{j=0}^k \mathrm{irf}(x, y, k)_j$$

This approach quantifies both the effect size and temporal dynamics of inter-variable influence, thus allowing ranking of variables by their net positive or negative impact on the individual's well-being over time (1706.09268).

2. Methodological Framework

The distinguishing aspect of AIRA-dojo lies in its fully automatic processing of individual time series:

• Data Ingestion: The system utilizes daily or intra-daily longitudinal data (e.g., diary entries, mobile sensor outputs) to capture within-person variability.
• Model Fitting: Separate VAR models are constructed for each individual, capturing their unique multivariate temporal dynamics.
• Simulation: Impulse responses are computed for all variables, simulating standard-deviation-scale perturbations and propagating effects forward over a user-defined horizon.
• Net Effect Estimation: The area under the IRF "curve" (cumulative effect) is used to compare and rank variables by their potential to effect desired change.
• Personalized Output: The entire process—model fitting, simulation, and advice extraction—takes less than one second for standard configurations and is amenable to both browser-based and node server deployment.

This methodological pipeline supports direct, individualized intervention planning (such as prioritizing behaviors or symptoms for self-modification), informed by one's own observed data dynamics (1706.09268).

3. Integration with Differentiable Physics and Control (Dojo)

AIRA-dojo extends beyond psychological time series modeling into differentiable physical simulation domains:

• Dojo Simulator: Originally conceived as an open-source differentiable physics engine, Dojo targets end-to-end learning tasks in contact-rich environments by modeling collision and frictional interactions as nonlinear complementarity problems (NCPs), and computes gradients via the implicit function theorem (2207.05060).
• Learning Optimal Control: The simulator supports optimization over control variables to minimize loss functions involving terminal and running costs, e.g.,

$\min \phi(s(T)) + \int_0^T L(s(t), u(t)) dt$

where the system state $s(t)$ experiences discrete jumps at contact events. Analytical solutions exist for simple settings, allowing direct validation of learned strategies against ground truth.

• Gradient Validation: Dojo's correct implementation of contact dynamics ensures that computed gradients (with respect to position, velocity, and control) closely match analytic derivatives as shown in canonical tasks (e.g., bouncing ball final height sensitivities).

This architecture enables learning from real-world or synthetic physical data, supports system identification and control synthesis, and underpins robotics pipelines requiring reliable differentiation through discontinuous contact events (2207.05060).

4. Practical Applications and Case Studies

AIRA-dojo accommodates a diverse range of real-world deployments:

Domain	Example Use	Specific Mechanisms
Personalized Health	Well-being advice from longitudinal self-report	Automated VAR/IRF + simulation
Digital Therapeutics	Immediate behavior feedback (e.g., web platforms)	Client/server JS & R packages
Robotic Simulation	Manipulation/planning with neural object models	Differentiable Dojo engine
System Identification	Estimation of mass/friction from video/telemetry	End-to-end gradient optimization

In digital health (1706.09268), AIRA has been deployed within studies such as HowNutsAreTheDutch, producing advice comparable in precision and utility to manual VAR/IRF analyses. In robotics, Dojo supports system identification from visual input (Neural Radiance Fields–derived models), and trajectory optimization for robotic manipulation, quantifying and minimizing dynamic mismatch through differentiable object/contact modeling (2210.09420).

5. Computational Efficiency and Scalability

AIRA-dojo systems are specifically architected for resource efficiency:

• Time Complexity: Core steps, notably cumulative effect computation across $m$ variables and $k$ horizon steps, scale as $O(m^3 k^3)$, which is further parallelizable (1706.09268).
• Hardware Requirements: Typical analyses (e.g., 6-variables, 20-step horizon) achieve sub-second execution times on commodity hardware, enabling desktop and cloud/browser integration.
• Implementation Languages: With main implementations in JavaScript for web compatibility and in R for statistical pipelines, deployments are practical at scales from single individuals to national e-health infrastructures.

Such characteristics support upscaling to large participant cohorts and on-the-fly adaptation for real-time feedback (1706.09268).

6. Validation and Comparison with Existing Techniques

AIRA's outputs have been systematically compared to prior manual analyses:

• Automated estimates of impulse effect magnitude and duration align closely with results from traditional IRF inspection, with discrepancies primarily linked to bootstrapping and interpolation method differences.
• Consistency is achieved via model refitting in standardized statistical libraries (e.g., R's vars package), demonstrating equivalence in dynamic effect estimation and, in some scenarios, improved precision through automated methodologies (1706.09268).
• In the differentiable physics setting, Dojo’s computed gradients are validated against analytical solutions, with the inclusion of time-of-impact corrections being crucial for physical consistency and control optimization validity (2207.05060).

AIRA-dojo thus attains the reliability of manual expert analysis within an automated framework, supporting precise, individualized recommendations and robust robotic control.

7. Future Directions and Broader Impact

AIRA-dojo represents a foundational paradigm in automated, individualized advice and optimization from time series data—whether in human-centric psychological domains or in differentiable robotic simulation. Future directions may include:

• Integration with adaptive intervention engines and digital therapeutics platforms for real-time feedback and intervention adjustment.
• Expansion to high-dimensional sensor arrays and multimodal data sources for personalized modeling in broader health and behavioral domains.
• Further enhancements in differentiable physics engines for complex, multi-agent, or deformable object scenarios.
• Widespread deployment in web-based infrastructures or embedded clinical decision support systems.

A plausible implication is that the methodological and computational templates established by AIRA-dojo could serve as a reference for future automated individualized modeling platforms across both behavioral health and robotic automation domains.