7 citations · 8 across the 9 of their papers we have counts for
9 papers
On Approaches to Building Surrogate ODE Models for Diffusion Bridges
Maria Khilchuk, Vladimir Latypov, Pavel Kleshchev +1
Diffusion and Schrödinger Bridge models have established state-of-the-art performance in generative modeling but are often hampered by significant computational costs and complex t…
Differentiation methods as a systematic uncertainty source in equation discovery
Maria Khilchuk, Ilya Markov, Alexander Hvatov
In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity…
Towards Universal Neural Operators through Multiphysics Pretraining
Mikhail Masliaev, Dmitry Gusarov, Ilya Markov +1
Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream l…
Knowledge-aware equation discovery with automated background knowledge extraction
Elizaveta Ivanchik, Alexander Hvatov
In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algo…
Towards stable real-world equation discovery with assessing differentiating quality influence
Mikhail Masliaev, Ilya Markov, Alexander Hvatov
This paper explores the critical role of differentiation approaches for data-driven differential equation discovery. Accurate derivatives of the input data are essential for reliab…
Directed differential equation discovery using modified mutation and cross-over operators
Elizaveta Ivanchik, Alexander Hvatov
The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control…
On the balance between the training time and interpretability of neural ODE for time series modelling
Yakov Golovanev, Alexander Hvatov
Most machine learning methods are used as a black box for modelling. We may try to extract some knowledge from physics-based training methods, such as neural ODE (ordinary differen…
Automated differential equation solver based on the parametric approximation optimization
Alexander Hvatov, Tatiana Tikhonova
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Never…
Partial differential equation solver based on optimization methods
Alexander Hvatov
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the…