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Deep neural networks have emerged as the workhorse for a large section ofrobotics and control applications, especially as models for dynamical systems.Such data-driven models are in turn used for designing and verifying autonomoussystems. They are particularly useful in modeling medical systems where datacan be leveraged to individualize treatment. In safety-critical applications,it is important that the data-driven model is conformant to establishedknowledge from the natural sciences. Such knowledge is often available or canoften be distilled into a (possibly black-box) model. For instance, an F1racing car should conform to Newton's laws (which are encoded within a unicyclemodel). In this light, we consider the following problem - given a model $M$and a state transition dataset, we wish to best approximate the system modelwhile being a bounded distance away from $M$. We propose a method to guaranteethis conformance. Our first step is to distill the dataset into a fewrepresentative samples called memories, using the idea of a growing neural gas.Next, using these memories we partition the state space into disjoint subsetsand compute bounds that should be respected by the neural network in eachsubset. This serves as a symbolic wrapper for guaranteed conformance. We arguetheoretically that this only leads to a bounded increase in approximationerror; which can be controlled by increasing the number of memories. Weexperimentally show that on three case studies (Car Model, Drones, andArtificial Pancreas), our constrained neurosymbolic models conform to specifiedmodels (each encoding various constraints) with order-of-magnitude improvementscompared to the augmented Lagrangian and vanilla training methods. Our code canbe found at: https://github.com/kaustubhsridhar/Constrained_Models

Guaranteed Conformance of Neurosymbolic Models to Natural Constraints