With the use of a universal nonlinear dynamic response (UNDR) function, models are trained using observed data to identify the continuum scale functional relationships between input sets and dynamic response curves. These models can then be used to predict dynamic response curves for input sets throughout the entire input domain. The UNDR function allows for models to be trained with relatively sparse amounts of observed data, while reducing the likelihood of overfitting and thereby increasing the predictive capability of the model.

The UNDR function is based implicitly on systems of nonlinear differential equations and is designed to accurately capture nonlinearities and yield dynamics in the form of time-course profiles. The universal nature of this unique formulation will allow for easier translation among models, reduce the need for model reduction, and eliminate the need for model selection.

This new tool can be applied to wide range of problems in science, engineering, and business. Examples shown here include pharmacokinetics (PK), pharmacodynamics (PD), combined PKPD, population PK, target-mediated drug disposition (TMDD), solute transport, partially-saturated fluid flow, friction stir welding, and real estate valuation models.

In the PKPD application, this approach allows for prediction of time-course PKPD profiles based on phenotypic properties of a popluation (population PKPD) as well as prediction of time-course profiles for members of the population for which data was not used to build the model (virtual patients). It is capable of multiple input compounds, multiple dose amounts, and multiple dosing times, and it automatically incorporates delay differential equations.

The ability to accurately predict nonlinear dynamics will allow for virtual screening to find input scenarios for a particular application that will yield a response that is optimal with respect to a desired outcome. The desired outcome can be based on a single objective function or a combination of various functions, in a multi-objective scenario. In the PKPD application, the objective could be PK, PD, or a combined PKPD model.

Examples of applications can be found on the Applications page.