Grunnleggende konsepter
The author proposes a Weak Collocation Regression method to reveal unknown stochastic dynamical systems with both α-stable Lévy noise and Gaussian noise, demonstrating accuracy and computational efficiency.
Sammendrag
The content discusses the application of Weak Collocation Regression (WCR) to infer stochastic dynamics with Lévy noise. The method is compared to existing approaches, showcasing improved accuracy and efficiency. Various multi-dimensional scenarios are explored, highlighting the effectiveness of WCR in distinguishing different types of noises.
The content emphasizes the importance of considering Lévy noise in stochastic systems due to its ability to capture heavy-tailed distributions and jumps. The experiments demonstrate the superior performance of WCR over previous methods in terms of accuracy and computational efficiency. Multi-dimensional problems are also addressed, showcasing the versatility of WCR in handling complex scenarios.
Key points include:
- Proposal of Weak Collocation Regression for inferring stochastic dynamics with Lévy noise.
- Comparison with existing methods showing improved accuracy and efficiency.
- Exploration of multi-dimensional problems highlighting the effectiveness of WCR.
- Importance of considering Lévy noise for capturing complex phenomena in stochastic systems.
Statistikk
Numerical experiments demonstrate that our method is accurate and computationally efficient.
Our approach can effectively identify two different types Gaussian and Lévy noise.
First, it requires fewer data points as the WCR method avoids an exponential increase in sample size as the dimensionality grows.
Accuracy. Our approach can effectively identify two different types Gaussian and Lévy noise.
Efficiency. First, it requires fewer data points as the WCR method avoids an exponential increase in sample size as the dimensionality grows.