ADVANCED COMPUTATIONAL PHYSICS

International Teaching ADVANCED COMPUTATIONAL PHYSICS

0522600059
DEPARTMENT OF PHYSICS "E. R. CAIANIELLO"
EQF7
PHYSICS
2021/2022

YEAR OF COURSE 1
YEAR OF DIDACTIC SYSTEM 2021
SECONDO SEMESTRE
CFUHOURSACTIVITY
324LESSONS
336LAB
Objectives
THE COURSE HAS THE OBJECTIVE OF CONSOLIDATING STUDENTS' TRAINING IN THE USE OF BASIC AND ADVANCED COMPUTATIONAL TOOLS NECESSARY TO STUDY PHYSICAL SYSTEMS, BUT ALSO STATISTICAL AND BIOLOGICAL ONES, FROM THE MOST SIMPLE TO THE MOST COMPLEX.

KNOWLEDGE AND UNDERSTANDING ABILITY
THE COURSE IS INTENDED TO PROVIDE THE STUDENT WITH ADVANCED KNOWLEDGE CONCERNING THE FUNDAMENTAL NUMERICAL METHODS FOR THE RESOLUTION OF DIFFERENT TYPES OF PROBLEMS IN PHYSICS AND THE ABILITY TO UNDERSTAND / LEARN BY ONESELF ADDITIONAL ADVANCEMENTS. IN PARTICULAR, THE STUDY OF ALGORITHMS FOR THE RESOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS IS PROVIDED, FOR THE IMPLEMENTATION OF THE FAST FOURIER TRANSFORM (FFT), FOR THE DIAGONALIZATION OF MATRICES, FOR THE GENERATION OF "PSEUDO-RANDOM" NUMBERS, FOR THE IMPLEMENTATION OF THE MONTE CARLO METHOD, FOR THE USE OF NEURAL NETWORKS, FOR THE SIMULATION OF REAL AND COMPLEX SYSTEMS. THE COURSE FORESEES THE USE OF C++ AS ADVANCED PROGRAMMING LANGUAGE AND THE LEARNING OF THE LANGUAGE SYNTAX AND OF THE DIFFERENT PARADIGMS OF PROGRAMMING (PROCEDURAL, MODULAR, OBJECT-ORIENTED) THAT IT SUPPORTS, SO THAT THE STUDENT CAN UNDERSTAND / LEARN BY ONESELF OTHER HIGH-LEVEL LANGUAGES.

ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING
THE COURSE IS INTENDED TO CONSOLIDATE STUDENT'S ABILITY TO SOLVE, AT A PROFESSIONAL LEVEL, PROBLEMS IN PHYSICS, BUT ALSO IN OTHER FIELDS OF SCIENCE, THROUGH THE USE OF NUMERICAL METHODS AND ALGORITHMS AND THEIR CODING IN TERMS OF COMPUTER PROGRAMS. IN PARTICULAR, THE STUDENT WILL HAVE TO RESTORE THE ABILITY TO SOLVE THE FUNDAMENTAL EQUATIONS OF MATHEMATICAL PHYSICS (HEAT, DIFFUSION, SCHRÖDINGER, ...), TO CALCULATE THE SUM OF SERIES OF PHYSICAL INTEREST THROUGH THE FFT, TO STUDY THE DYNAMICS OF INTERACTING QUANTUM SYSTEMS THROUGH THE LANCZOS METHOD, TO USE THE MONTE CARLO METHOD TO CALCULATE INTEGRALS IN MULTI-DIMENSIONAL SPACES, TO SIMULATE COMPLEX SYSTEMS AND EXPERIMENTAL EQUIPMENT, PROPAGATE THE ERRORS OF EXPERIMENTAL VERY COMPLEX MEASURES. THE STUDENT WILL ALSO ACHIEVE AN ADVANCED KNOWLEDGE OF THE C++ LANGUAGE FOR THE CONCRETE APPLICATION OF THE CONCEPTS ACQUIRED.
Prerequisites
THE KNOWLEDGE OF THE BASIC CONCEPTS OF CLASSICAL AND MODERN PHYSICS, CLASSICAL AND QUANTUM STATISTICAL MECHANICS, AND MATHEMATICAL ANALYSIS AND PHYSICS.
Contents
1. ADVANCED METHODS: SPLINES, MINIMUM SQUARES, GAUSSIAN INTEGRATION, OPTIMIZATION AND SEARCH FOR ZEROS IN MORE DIMENSIONS, ANNEALING AND TEMPERING. APPLICATION TO PHYSICAL PROBLEMS (8 HOURS).
2. DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS: HEAT, DIFFUSION, SCHRÖDINGER EQUATIONS. APPLICATION TO PHYSICAL PROBLEMS (6 HOURS).
3. FAST FOURIER TRANSFORM (FFT): SERIES OF PHYSICAL INTEREST (MATSUBARA, ...), SPECTRAL ANALYSIS. APPLICATION TO PHYSICAL PROBLEMS (6 HOURS).
4. DIAGONALIZATION OF MATRICES: LANCZOS ALGORITHM FOR QUANTUM INTERAGENT SYSTEMS AND DENSITY MATRIX. APPLICATION TO PHYSICAL PROBLEMS (6 HOURS).
MACHINE LEARNING: BASIC NOTIONS. EXAMPLES ON POLYNOMIAL REGRESSION AND AUTONOMOUS DEVELOPMENT OF THE ASSOCIATED NUMERICAL CODES. COST FUNCTION. BIAS-VARIANCE DECOMPOSITION. GRADIENT DESCENT AND ITS GENERALISATIONS TO SEARCH MINIMA OF A COST FUNCTION. INTRODUCTION TO BAYESIAN INFERENCE. LINEAR REGRESSION AND ITS BAYESIAN FORMULATION. REGULARISATION. APPLICATIONS: LEARNING THE COUPLING CONSTANTS OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. CLASSIFICATION TASKS. PERCEPTRON. LOGISTIC REGRESSION. CROSS-ENTROPY AND SOFT-MAX REGRESSION. APPLICATIONS: DETECTION OF THE PHHASE OF AN ISING MODEL. AUTONOMOUS DEVELOPMENT OF THE RELATED NUMERICAL CODES. NEURAL NETWORKS: ARCHITECTURE AND TRAINING. FEEDFORWARD AND BACKPROPAGATION ALGORITHM. APPLICATIONS: AUTONOMOUS DEVELOPMENT OF NUMERICAL CODES FOR THE PROBLEMS ASSOCIATED TO POLYNOMIAL REGRESSION AND TO THE ISING MODEL. EXAMPLES USING PRE-BUILT PACKAGES (MATHLAB) ENFORCING CONVOLUTIONAL NEURAL NETWORKS. (20 HOURS).
6. MONTE CARLO METHOD: GENERATION OF PSEUDO-RANDOM NUMBERS, CALCULATION OF MULTI-DIMENSIONAL INTEGRALS, SIMULATION OF COMPLEX SYSTEMS AND EXPERIMENTAL SET UP. PROPAGATION OF ERRORS IN COMPLEX EXPERIMENTAL MEASURES. APPLICATION TO PHYSICAL PROBLEMS (15 HOURS).
7. C++ LANGUAGE (5 HOURS).
8. PYTHON LANGUAGE (5 HOURS).
Teaching Methods
THE COURSE INCLUDES 24 HOURS OF FRONTAL LECTURES IN CLASSROOM FINALIZED TO THE LEARNING OF THE ADVANCED KNOWLEDGE ABOUT NUMERICAL METHODS AND PROGRAMMING AND 36 HOURS OF FRONTAL PRACTICAL LECTURES IN LABORATORY FOCUSED ON THE ILLUSTRATION OF THE PROCESS OF MODELING THE PHYSICAL PROBLEM UNDER CONSIDERATION, THE SELECTION AND DEVELOPMENT OF NUMERICAL METHODS AND ALGORITHMS NECESSARY FOR ITS NUMERICAL SOLUTION, THE DESIGN OF THE CODE ACCORDING TO THE CHOSEN PROGRAMMING PARADIGM, THE CONCRETE DRAFTING OF THE CODE IN C++ (SYNTAX OF THE LANGUAGE), ITS COMPILATION, EXECUTION, AND RELATED COLLECTION AND GRAPHICAL REPRESENTATION OF THE RESULTS.
Verification of learning
THE ASSESSMENT AND EVALUATION OF THE STUDENT'S LEVEL OF LEARNING WILL TAKE PLACE THROUGH A FINAL TEST THAT WILL CONSIST IN THE ORAL DISCUSSION OF A RESEARCH PROJECT, ASSIGNED AT THE END OF THE COURSE TO A GROUP OF TWO/THREE STUDENTS, CONCERNING THE SOLUTION OF A PHYSICAL PROBLEM NOT MENTIONED IN THE COURSE, BUT SOLVED BY THE NUMERICAL METHODS COVERED DURING THE COURSE. THE ORAL DISCUSSION IS AIMED AT ASSESSING THE LEVEL OF THEORETICAL KNOWLEDGE, THE AUTONOMY OF ANALYSIS AND JUDGMENT, AS WELL AS THE STUDENT'S PRESENTATION SKILLS.

THE EVALUATION LEVEL IS ASSIGNED TAKING INTO ACCOUNT THE EFFICIENCY OF THE METHODS USED, THE COMPLETENESS AND ACCURACY OF THE ANSWERS, AS WELL AS THE CLARITY IN THE PRESENTATION.

THE MINIMUM LEVEL OF EVALUATION (18) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES UNCERTAINTIES IN THE APPLICATION OF NUMERICAL METHODS AND IN THE IDENTIFICATION OF METHODS TO CONTROL NUMERICAL ERROR, AND HAS A LIMITED KNOWLEDGE OF THE MAIN ALGORITHMS.

THE MAXIMUM LEVEL (30) IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND IN-DEPTH KNOWLEDGE OF NUMERICAL METHODS AND ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY AND MANAGE THE SOURCES OF NUMERICAL ERROR PRESENT IN THE SPECIFIC PROBLEM HE/SHE HAS CHOSEN TO DEAL WITH.

PRAISE IS GIVEN WHEN THE CANDIDATE DEMONSTRATES SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENT AND SHOWS HOW TO PRESENT THE TOPICS WITH CONSIDERABLE MASTERY OF THE SPECIFIC TECHNICAL LANGUAGE AND AUTONOMOUS PROCESSING SKILLS EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.
Texts
COMPUTATIONAL PHYSICS: T. PANG; AN INTRODUCTION TO COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 2ND ED. (2006), CODICI IN FORTRAN 90: 1ST ED. (1997). N.J. GIORDANO; COMPUTATIONAL PHYSICS; BENJAMIN CUMMINGS; 2ND ED. (2005). J. THIJSSEN; COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2007). R.H. LANDAU, J. PAEZ, C.C. BORDEIANU; A SURVEY OF COMPUTATIONAL PHYSICS: INTRODUCTORY COMPUTATIONAL SCIENCE; PRINCETON UNIVERSITY PRESS (2008). P.L. DEVRIES , J.E. HASBUN; A FIRST COURSE IN COMPUTATIONAL PHYSICS; JONES & BARTLETT PUBLISHERS; 2ND ED. (2010). A. KLEIN; INTRODUCTORY COMPUTATIONAL PHYSICS; CAMBRIDGE UNIVERSITY PRESS; 2ND ED. (2010). R. FITZPATRICK; COMPUTATIONAL PHYSICS; LECTURE NOTES.
MATHEMATICAL METHODS: K.F. RILEY, M.P. HOBSON, AND S.J. BENCE; MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING; CAMBRIDGE UNIVERSITY PRESS; 3RD ED. (2006). S. HASSANI; MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS; SPRINGER SCIENCE+BUSINESS MEDIA, LLC; 2ND ED. (2009). H. SHIMA, AND T. NAKAYAMA; HIGHER MATHEMATICS FOR PHYSICS AND ENGINEERING; SPRINGER-VERLAG (2010).
NUMERICAL METHODS AND ALGORITHMS: W.H. PRESS, S.A. TEUKOLSKY, H.A. BETHE, W.T. VETTERLING, AND B.P. FLANNERY; NUMERICAL RECIPES - THE ART OF SCIENTIFIC COMPUTING; CAMBRIDGE UNIVERSITY PRESS; CONTENUTI: 3RD ED. (2007). A HIGH-BIAS,LOW-VARIANCE INTRODUCTION TO MACHINE LEARNING FOR PHYSICISTS: P.METHA, M. BUKOV, C-H. WANG, A.G.R. DAY, C. RICHARDSON, C.K. FISHER, D.J. SCHWAB (HTTPS://ARXIV.ORG/ABS/1803.08823). NOTES OF THHE LECTURER ON MACHINE LEARNING.
More Information
THE ATTENDANCE, ALTHOUGH NOT MANDATORY, IT IS STRONGLY RECOMMENDED. FOR A SATISFACTORY PREPARATION, IT IS REQUIRED, ON AVERAGE, TWO HOURS OF STUDY FOR EACH HOUR OF CLASS, BOTH FRONTAL AND LABORATORY ONES.
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