Behavior prediction with dynamic adaptation to environmental conditions

A method for training a neural network for modelling time-series data, the method comprising:

• inputting time-series data into the neural network to train a testing model including a plurality of model parameters;
• evaluating the testing model utilizing a plurality of hyper-forgetting rates to select a best performing hyper-forgetting rate from the plurality of hyper-forgetting rates;
• testing a model optimization using the best performing hyper-forgetting rate with the testing model to test combinations of hyper-parameters for training the neural network to select a best performing combination of hyper-parameters for training the neural network;
• determining an error of the testing model using the model optimization with best performing hyper-parameters according to least squares regression;
• recursively update the model parameters of the neural network according to the least squares regression by determining a pseudo-inverse of a Hessian of the least squares regression at a current time stamp, including:
• generating a projection of the time-series data at a current time stamp, the projection being orthogonal to a kernel of the Hessian at a previous time stamp;
• determining that the projection is not equal to zero;
• determining the pseudo-inverse of the Hessian at the current time stamp according to the projection, the kernel and the inverse of the Hessian at a previous time-stamp;
• determining optimum model parameters according to the Hessian at the current time stamp and a negative gradient of the least squares regression;
• predicting a next step behavior of the time-series data using the optimum model parameters;
• storing the next step behavior in a database for access by a user;
• and
• updating the model in the memory with the updated model parameters.

A system for training a neural network for modelling time-series data, the system comprising:

• inputting time-series data into the neural network to train a testing model including a plurality of model parameters;
• a testing model to test a plurality of hyper-forgetting rates, select a best performing hyper-forgetting rate from the plurality of hyper-forgetting rates, test a model optimization using the best performing hyper-forgetting rate with the testing model to test combinations of hyper-parameters and select a best performing combination of hyper-parameters;
• an optimization system to determine an error of a testing model stored in memory using the best performing hyper-parameters;
• a parameter updater to recursively update the model parameters of the neural network according to the least squares regression by determining a pseudo-inverse of a Hessian of the least squares regression at a current time stamp using a pseudo-inversion mechanism according to a projection of the time-series data at the current time stamp and the pseudo-inverse of the Hessian at a previous time-stamp to determine optimum model parameters and updated the linear model in the memory with the updated model parameters;
• a behavior modeler that predicts a next step behavior of the time-series data according to the updated model parameters;
• and
• a database in communication with the memory and the parameter updater to store the next step behavior in a database for access by a user.