We show the similarities between our method, Neural ODE, and differentiable physics in Figure 4. All the three approaches have a differentiable system governed by some kinds of differential equations. Our method parametrizes the dynamics using continuous basis functions; Neural ODE uses neural networks; and Differentiable physics describes the dynamics system using physics equations like Newton's Second Law, Navier-Stokes equations. Let Uv(t2,t1) be as defined in Theorem 3.2. Let Lbe defined as (4), and H(v,t) = P jfj(v,t)Hj.

Wepropose alearning algorithm which accounts for potential biases held by external decision-makers in a system.

Clearly, with only 26M learnable parameters, the performance can be boosted from 79.9 to 84.4

Source code for the training pipeline, tasks, and models used in this work, is available as part of the supplementary material. We used the same Adam [48] optimizer for all our experiments and a learning rate of 0.001, and a batch size of 128. For solving the differential equations both during ground truth data generation as well as with the neural ODEs, we use the Tsitouras 5/4 Runge-Kutta (Tsit5) method from DifferentialEquations.jl [36]. A.1 Coupled Pendulum The coupled pendulum dynamics are defined as We train the MP-NODE on a dataset of 500 trajectories, each randomly initialized with state values between [ π/2, π/2] for the θ and [ 1, 1] for θ, with a time step of 0.1s and each trajectory 10s long. The dataset is normalized through Z-score normalization.