Systems and methods of applying tensor radial basis function networks to machine learning

A system for embedding ordinary differential equations into tensor radial basis networks comprising at least one processor configured to:

• receive a tensored basis function having D dimensions and coefficients A_d, B_d, and C_d, where A_d is a zeroth-derivative coefficient for zeroth-derivative terms, B_d is a first-derivative coefficient for first-derivative terms, and C_d is a second-derivative coefficient for second-derivative terms;
• define A_hat as a function of A and D, B_hat as a function of A, B, and D, and C_hat as function of A, C, and D;
• define an orthogonal exotic algebra a, b, c;
• apply a, b, and c, along with A_hat, B_hat, and C_hat, as coefficients for the zeroth-derivative, first-derivative, and second-derivative terms, respectively, thereby generating an updated tensored basis function;
• and
• embed the updated tensored basis function by forming a matrix product state (MPS) and training the MPS.