Work programme
Work programme for period 1
| Tasks | Participating researchers | Duration (months) | Expected results |
|---|---|---|---|
| WP 1 Modeling the gravitational-wave ringing signal of black holes in general relativity and modified gravity by physically informed neural networks | Stoycho Yazadjiev, Angela Slavova, Yavor Markov, Dimitar Popchev, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
9 | Obtaining accurate solutions of the obtained models. The results will be published in 5 papers in the peer-reviewed journals (Q1, Q2) and in 3 papers in the conference proceedings with SJR |
| 1.1 Modeling the gravitational-wave ringing signal of black holes by physically informed neural networks | Stoycho Yazadjiev, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
3 | Obtaining the relevant partial differential equations and constructing physically informed neural networks (PINN) to solve them |
| 1.2 Development of algorithms based on the obtained FINM models by integrating the mathematical model into the network | Angela Slavova, Yavor Markov, Dimitar Popchev, Kalin Staykov, Daniela Doneva, Galin Gyulchev |
3 | Parameterization of PINN and obtaining the corresponding approximation after their training |
| 1.3 Optimization of PINN parameters | Stoycho Yazadjiev, Kalin Staykov, Daniela Doneva, Angela Slavova, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
3 | Computer simulations and validation |
| WP 2 Modeling the ringing gravitational-wave signal of compact non-horizontal objects (neutron stars, boson-fermion stars, topological solitons) by physically informed neural networks | Stoycho Yazadjiev, Angela Slavova, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
9 | Obtaining accurate solutions of the obtained models. The results will be published in 4 papers in the peer-reviewed journals (Q1, Q2) and in 4 papers in the conference proceedings with SJR |
| 2.1 Modeling the gravitational-wave ringing signal of neutron stars, boson-fermion stars, topological solitons by PINN | Stoycho Yazadjiev, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
3 | Obtaining the model partial differential equations with the corresponding boundary conditions |
| 2.2 Development of algorithms for approximating differential equations by finding the multiple parameters of PINN | Angela Slavova, Kalin Staykov, Daniela Doneva, Galin Gyulchev |
3 | Obtaining optimal parameters through the developed algorithms |
| 2.3 Loss function optimization by limiting the space of acceptable parameters | Angela Slavova, Kalin Staykov, Daniela Doneva, Galin Gyulchev |
3 | Minimizing error from computer simulations and validation |
| WP 5 Wide dissemination of project research results | Stoycho Yazadjiev, Angela Slavova, Borislav Yordanov, Venelin Todorov, Yavor Markov, Dimitar Popchev, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
33 | Generation of a package of innovative knowledge, research software and interpretation of the obtained new effects in the proposed models and their dissemination |
| 5.1 Generating knowledge as a result of the scientific activity of the project team through teaching | 33 | Organization of groups and seminars to strengthen knowledge in the field of scientific research | |
| 5.2 Dissemination of knowledge by reporting the obtained results at national and international scientific conferences | 33 | Improving connections between young scientists and leading scientists in the country and Europe | |
| 5.3 Exchange and dissemination of knowledge through the development of a database with open access to the project page | 33 | Creation of a web page for virtual access to the main results of the project implementation and the created software |
Work programme for period 2
| Tasks | Participating researchers | Duration (months) | Expected results |
|---|---|---|---|
| WP 3 Application of physically informed neural networks to solve differential equations with unknown parameters that can be determined from observational data or experimental observations with noise | Angela Slavova, Stoycho Yazadjiev, Borislav Yordanov, Venelin Todorov, Daniela Doneva, Yavor Markov, Dimitar Popchev, Kalin Staykov |
9 | Obtaining accurate solutions of the relevant differential equations. The results will be published in 4 papers in the peer-reviewed journals (Q1, Q2) and in 5 papers in the conference proceedings with SJR |
| 3.1 Solving the inverse problem of finding the unknown parameters of partial differential equations by physically informed neural networks | Angela Slavova, Stoycho Yazadjiev, Borislav Yordanov, Venelin Todorov, Daniela Doneva, Yavor Markov, Dimitar Popchev |
3 | Development of algorithms for network parameterization and loss function minimization |
| 3.2 Optimizing network parameters and obtaining approximation solutions | Angela Slavova, Stoycho Yazadjiev, Venelin Todorov, Daniela Doneva, Yavor Markov, Dimitar Popchev, Kalin Staykov |
3 | Obtaining the model parameters from observable data |
| 3.3 Training the network without using labeled data from before the simulations | Angela Slavova, Venelin Todorov, Yavor Markov, Dimitar Popchev |
3 | Computer simulations and validation |
| WP 4 Development of machine learning algorithms using PINN as universal function approximators for solving complex hyperbolic equations on distorted space-time manifolds | Angela Slavova, Stoycho Yazadjiev, Borislav Yordanov, Venelin Todorov, Daniela Doneva, Yavor Markov, Dimitar Popchev, Kalin Staykov |
9 | Obtaining new machine learning algorithms for PINN. The results will be published in 6 papers in the peer-reviewed journals (Q1, Q2) and in 4 papers in the conference proceedings with SJR |
| 4.1 Development of universal approximators for solving complex hyperbolic equations on distorted space-time manifolds | Angela Slavova, Stoycho Yazadjiev, Venelin Todorov, Daniela Doneva, Yavor Markov, Dimitar Popchev |
3 | Reducing the problem to a loss function optimization problem |
| 4.2 Development of PINN algorithms by strengthening the loss function of the corresponding equation | Angela Slavova, Stoycho Yazadjiev, Venelin Todorov, Daniela Doneva, Kalin Staykov, Yavor Markov, Dimitar Popchev |
3 | Optimal approximation of PINN parameters |
| 4.3 Machine learning of model parameters by transforming them into training points to improve the quality of predictions | Angela Slavova, Venelin Todorov, Yavor Markov, Dimitar Popchev |
3 | Computer simulations and validation |
| WP 5 Wide dissemination of project research results | Stoycho Yazadjiev, Angela Slavova, Borislav Yordanov, Venelin Todorov, Yavor Markov, Dimitar Popchev, Kalin Staykov, Daniela Doneva, Petar Yordanov, Valentin Deliyski, Galin Gyulchev, Petya Nedkova |
33 | Generation of a package of innovative knowledge, research software and interpretation of the obtained new effects in the proposed models and their dissemination |
| 5.1 Generating knowledge as a result of the scientific activity of the project team through teaching | 33 | Organization of groups and seminars to strengthen knowledge in the field of scientific research | |
| 5.2 Dissemination of knowledge by reporting the obtained results at national and international scientific conferences | 33 | Improving connections between young scientists and leading scientists in the country and Europe | |
| 5.3 Exchange and dissemination of knowledge through the development of a database with open access to the project page | 33 | Creation of a web page for virtual access to the main results of the project implementation and the created software |