In 2019, Raissi et al. introduced Physics-Informed Neural Networks (PINNs), a methodology which sought to combine the power of Neural Networks as universal function approximators and our knowledge of physics in order to solve ODEs, PDEs that appear in physical problems. Additional advancements in this field led to the creation of Neural Operators (NOs), which are even more powerful as they are universal operator approximators. Both NNs and NOs have advantages over traditional numerical methods, as they can be trained using both physical knowledge and data, can tackle high-dimensional and parametric problems, and through automaticdifferentiation can calculate exact numerical gradients quickly. Modeling the sliding of seismic plates against each other is a difficult problem, as developing a friction framework is not straightforward, nor is solving the differential system of equations which result from it. The rate-and-state formulation offers a way to model the sliding of two plates as a function the relative velocity of the two bodies and the state variable θ which characterizes the sliding interface. However, this formulation consists of two coupled differential equations, where velocity changes can cause stark changes in θ, making it difficult to solve with traditional numerical methods. In this project, we seek to leverage PINNs and Neural Operators to solve two distinct friction-related problems: • PINNs will be used to solve an initial-value problem of a sliding system subjected a to constant load velocity. • Neural Operators will be used to learn the a constitutive law for friction through a function to function mapping between the loading velocity function and the friction coefficient function. This report is organized in several chapters. Chapter 2 goes over the fundamentals of the friction model we will be using. Chapter 3 will cover neural networks, how they can be turned into PINNs, and the required considerations when using PINNs. Chapter 4 will demonstrate the set-up and results for the forward problem solved by the PINN. Chapter 5 does a brief overview of Neural Operators and shows initial experiments in their use for function-to-function mapping. Chapter 6 reflects on the project and offers avenues for future work.