Modeling complex dynamical systems poses significant challenges, with traditional methods struggling to work on a variety of systems and scale to high-dimensional dynamics. In response, we present DynaDojo, a novel benchmarking platform designed for data-driven dynamical system identification. DynaDojo provides diagnostics on three ways an algorithm's performance scales: across the number of training samples, the complexity of a dynamical system, and a target error to achieve. Furthermore, DynaDojo enables studying out-of-distribution generalization (by providing unique test conditions for each system) and active learning (by supporting closed-loop control). Through its user-friendly and easily extensible API, DynaDojo accommodates a wide range of user-defined \texttt{Algorithms}, \texttt{Systems}, and \texttt{Challenges} (evaluation metrics).

Modeling complex dynamical systems poses significant challenges, with traditional methods struggling to work on a variety of systems and scale to high-dimensional dynamics. In response, we present DynaDojo, a novel benchmarking platform designed for data-driven dynamical system identification. DynaDojo provides diagnostics on three ways an algorithm's performance scales: across the number of training samples, the complexity of a dynamical system, and a target error to achieve. Furthermore, DynaDojo enables studying out-of-distribution generalization (by providing unique test conditions for each system) and active learning (by supporting closed-loop control). Through its user-friendly and easily extensible API, DynaDojo accommodates a wide range of user-defined \texttt{Algorithms}, \texttt{Systems}, and \texttt{Challenges} (evaluation metrics).

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized zeroth-order Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint maximum \textit{a~posteriori} (JMAP) and variational Bayesian approximation (VBA), are compared to the popular SINDy algorithm for thresholded least-squares regression, by application to several dynamical systems with added noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or ``Gaussian norm'' $||\vy-\hat{\vy}||^2_{M^{-1}} = (\vy-\hat{\vy})^\top {M^{-1}} (\vy-\hat{\vy})$, where $\vy$ is a vector variable, $\hat{\vy}$ is its estimator and $M$ is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection.