Belangrijkste concepten
A method combining Gaussian process regression and sparse identification of nonlinear dynamics (SINDy) to learn accurate analytical models of nonlinear dynamical systems from sparse and noisy data.
Samenvatting
The paper addresses the challenge of deriving dynamical models from sparse and noisy data. It proposes a method called GPSINDy that combines Gaussian process regression and the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to denoise the data and identify nonlinear dynamical equations.
Key highlights:
- Gaussian process regression is used to smooth and interpolate the sparse, noisy state measurements, providing better estimates of the state derivatives for symbolic regression.
- The smoothed state and derivative estimates are then used in the LASSO optimization problem of SINDy to discover the governing equations.
- The method is benchmarked on a Lotka-Volterra model, a unicycle dynamic model in simulation, and hardware data from an NVIDIA JetRacer system.
- Experiments show GPSINDy outperforms baselines like standard SINDy and neural network-based methods, achieving up to 61.92% improvement in predicting future trajectories from the discovered dynamics.
- The novelty lies in the use of Gaussian processes to smooth the state measurements and compute the state derivatives, which improves the robustness of symbolic regression to noise and data sparsity.
Statistieken
The Lotka-Volterra model has the following true coefficients: a = 1.1, b = 0.4, c = 1.0, d = 0.4.
For the unicycle model, the control inputs are u1(t) = sin(t) and u2(t) = 0.5 cos(t).
The NVIDIA JetRacer data was collected at 50 Hz for 22.85 seconds, with the state consisting of x-y position, forward velocity, and heading angle.
Citaten
"Our simple approach offers improved robustness with sparse, noisy data compared to SINDy alone."
"Gaussian process regression is particularly effective as an interpolation tool and at reducing the noise in measurement data."
"GPSINDy consistently outperforms the baselines across all noise magnitudes, highlighting its robustness in dealing with noisy data."