Applications of Autonomous Computational Methods for Finding - PowerPoint PPT Presentation

Applications of Autonomous Computational Methods for Finding Step-by-Step Solutions A. Pownuk The University of Texas at El Paso, El Paso, Texas, USA 23rd Joint UTEP/NMSU Workshop on Mathematics, Computer Science, and Computational Sciences 1 / 21

Outline Online Learning 1 Automatically Generated Examples 2 New Computational Methods 3 Self-Adaptive and Autonomous Computational Methods 4 Conclusions 5 2 / 21

Online Learning Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 3 / 21

Online Learning Online Learning Automatically Generated Examples New Computational Sharing the lecture notes. Methods Interactive platform for doing online homework. Self-Adaptive and Autonomous Automated system for checking attendance. Computational Methods Integrated response system. Conclusions Grades management system. Interactive projects. 4 / 21

Automatically Generated Examples Online Learning Automatically It is necessary to explain as basic mathematical/scientific Generated Examples concepts in details. New Student’s can compare their work with available examples. Computational Methods Automatically generated examples can be used as sample Self-Adaptive and assignments in on-line homework, exams, and ungraded Autonomous Computational assignments. Methods Automatically generated examples can be related to many Conclusions different methods for solutions. It is possible to crated millions examples in a very short time . If all inference rules are done properly, then the examples are without errors. . 5 / 21

Example (differentiation) Online Learning Automatically Generated Examples Table of basic formulas for differentiation. New Computational Product rule, quotient rule, chain, rule etc.. Methods Self-Adaptive Rules for simpling expression. and Autonomous Automatically generated examples can be related to many Computational Methods different methods for solutions. Conclusions Knowledge available to the system is in the format which is almost exactly the same like in the regular textbooks (no machine learning ...). 6 / 21

Example (differentiation) Online Learning Automatically Sample formulas Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 7 / 21

Example Online Learning Automatically Generated Examples Sample results New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 8 / 21

Example (Latex source) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 9 / 21

Step by Step Solution Online Learning Wolpharm Alpha Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 10 / 21

Differentiation (step 1) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 11 / 21

Differentiation (step 2) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 12 / 21

Differentiation (step 3) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 13 / 21

Differentiation (step 4) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 14 / 21

Differentiation (step 5) Online Learning Automatically Generated Examples New Computational Methods Self-Adaptive and Autonomous Computational Methods Conclusions 15 / 21

New Computational Methods Online Learning Automatically Generated Examples Available information. New Computational Linear equation with one variable. Methods Self-Adaptive and 2 + x = 4 Autonomous Computational Methods Solution Conclusions x = 2 Knowledge base of mathematical operations, theorems, etc. 16 / 21

Solution Online Learning Automatically Generated Examples Solution procedure computed automatically based on available New knowledge. Computational Methods 2 + x = 4 Self-Adaptive and x + 2 − 2 = 4 − 2 Autonomous Computational Methods x + 0 = 2 Conclusions x = 2 Now it is possible to create new solution procedure based on presented algorithm and use it for solution of other problems, etc. 17 / 21

Integration Online Learning Problem Automatically Generated Examples � (2 x + 1) dx New Computational Rules for integration, theorems, algebraic rules, etc. Methods Self-Adaptive Solution and Autonomous � (2 x + 1) dx Computational Methods � � 2 xdx + 1 dx Conclusions � 2 xdx + x 2 x 2 2 + x + C Now it is possible to implement this method as a new procedure and use it in the future. 18 / 21

Self-Adaptivity Online Learning The system is fully autonomous. All changes in the Automatically program can be done automatically without interaction Generated Examples with the user. New All changes of the code of the program can be done Computational Methods during the runtime. Self-Adaptive System is distributed and can work independently on many and Autonomous computers which improve reliability of the system. Computational Methods Once information is added to the system it will never be Conclusions forgotten and can be reused in the future in order to create new (improved) knowledge. Presented methodology can be applied not only to mathematical problems but also to any other scientific field which can be described by some abstract concepts (e.g. statistics, engineering, chemistry, biology, computer science etc.). 19 / 21

Imaginary Universe of Scientific Knowledge Online Learning “Imaginary Universe” terms used by some MIT researchers. Automatically Generated Quantum Artificial Life in an IBM Quantum Computer Examples (U. Alvarez-Rodriguez, M. Sanz, L. Lamata & E. Solano). New Computational Scientific Reports volume 8, Article number: 14793 (2018) Methods Self-Adaptive Mathematical/scientific knowledge can be treated as and Autonomous independent units that can interact with each-other and Computational Methods create new, possibly useful knowledge. Conclusions Generation of new knowledge can be fully automated and autonomous. No interaction with humans is necessary. Development of new knowledge is possible in many different fields (e.g. statistics, engineering, chemistry, biology, computer science etc.). 20 / 21

Conclusions Online Learning Automatically Generated Examples By using presented methodology it is possible to create New complex educational examples in many areas of Computational Methods mathematics as well as in other areas of science and Self-Adaptive engineering. and Autonomous In a few minutes it is possible to create thousands pages Computational Methods with typical examples without interaction with humans Conclusions and that can be used in education. By using self adaptive computational methods it is possible to automatically generate new mathematical theorems completely independently from human interactions. 21 / 21