HopCast: Calibration of Autoregressive Dynamics Models

Deep learning models are often trained to approximate dynamical systems that can be modeled using differential equations. These models are optimized to predict one step ahead and produce calibrated predictions if the predictive model can quantify uncertainty, such as deep ensembles. At inference time, multi-step predictions are generated via autoregression, which needs a sound uncertainty propagation method (e.g., Trajectory Sampling) to produce calibrated multi-step predictions. This paper introduces an approach named HopCast that uses the Modern Hopfield Network (MHN) to learn the residuals of a deterministic model that approximates the dynamical system. The MHN predicts the density of residuals based on a context vector at any timestep during autoregression. This approach produces calibrated multi-step predictions without uncertainty propagation and turns a deterministic model into a calibrated probabilistic model. This work is also the first to benchmark existing uncertainty propagation methods based on calibration errors with deep ensembles for multi-step predictions.

Towards Robust Car Following Dynamics Modeling via Blackbox Models: Methodology, Analysis, and Recommendations

The selection of the target variable is important while learning parameters of the classical car following models like GIPPS, IDM, etc. There is a vast body of literature on which target variable is optimal for classical car following models, but there is no study that empirically evaluates the selection of optimal target variables for black-box models, such as LSTM, etc. The black-box models, like LSTM and Gaussian Process (GP) are increasingly being used to model car following behavior without wise selection of target variables. The current work tests different target variables, like acceleration, velocity, and headway, for three black-box models, i.e., GP, LSTM, and Kernel Ridge Regression. These models have different objective functions and work in different vector spaces, e.g., GP works in function space, and LSTM works in parameter space. The experiments show that the optimal target variable recommendations for black-box models differ from classical car following models depending on the objective function and the vector space. It is worth mentioning that models and datasets used during evaluation are diverse in nature: the datasets contained both automated and human-driven vehicle trajectories; the black-box models belong to both parametric and non-parametric classes of models. This diversity is important during the analysis of variance, wherein we try to find the interaction between datasets, models, and target variables. It is shown that the models and target variables interact and recommended target variables don't depend on the dataset under consideration.