Stochastic Methods in Scientific Computing
portes grátis
Stochastic Methods in Scientific Computing
From Foundations to Advanced Techniques
Lucini, Biagio; D'Elia, Massimo; Langfeld, Kurt
Taylor & Francis Inc
06/2024
382
Dura
Inglês
9781498796330
15 a 20 dias
Descrição não disponível.
1. Random Numbers. 1.1. Random numbers and probability distribution. 1.2. Central limit theorem. 1.3. Beyond the Normal distribution. 1.4. Exercises. 2. Random walks. 2.1. Random walk as a Markov process. 2.2. Random walks in 1 and 2 dimensions. 2.3. Levy flight. 2.4. Random walks with potentials. 2.5. Exercises. 3. Monte Carlo methods. 3.1. Objectives and concepts. 3.2. Monte-Carlo integration. 3.3. Markov Chain Monte-Carlo. 3.4. Advanced Error Analysis Techniques. 3.5. Error estimate in the presence of autocorrelation. 3.6. Error estimate for non-trivial estimators: The Jackknife, and the Bootstrap. 3.7. Biased Estimators. 3.8. Exercises. 4. Statistical models. 4.1. An introduction to thermodynamics. 4.2. From thermodynamics to statistical mechanics. 4.3. Phase transitions. 4.4. The Ising model. 4.5. An overview of other models. 4.6. Exercises. 5. Advanced Monte-Carlo simulation techniques. 5.1. Hamiltonian (Hybrid) Monte-Carlo (HMC) simulations. 5.2. Non-local Monte-Carlo update. 5.3. Micro-canonical simulations. 5.4. Flat histogram methods. 5.5. The Linear Logarithmic Relaxation (LLR) method. 5.6. Exercises. 6. From Statistical Systems to Quantum Field Theory. 6.1. Invitation: The O(2) model. 6.2. The Bridge to QFT: the Feynman path-integral. 6.3. Gauge Theories. 6.4. Adding fermion fields. 6.5. Exercises. 7. Current challenges in Monte-Carlo Simulations. 7.1. Sign and overlap problems. 7.2. Introduction to overlap problems. 7.3. Estimating probability density functions. 8. Data Analytics and Statistical Systems. 8.1. Model regression - L2 norm. 8.2. Gaussian Process. 8.3. Machine learning with graphs. 8.4. Emulation of statistical systems with Machine Learning. 8.5. Categorisation in statistical physics: Naive Bayes. 8.6. Machine learning classification of phase transitions.
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Random walks;Monte Carlo methods;Monte-Carlo integration;2D Ising model;Langevin simulations;High-Performance Computing
1. Random Numbers. 1.1. Random numbers and probability distribution. 1.2. Central limit theorem. 1.3. Beyond the Normal distribution. 1.4. Exercises. 2. Random walks. 2.1. Random walk as a Markov process. 2.2. Random walks in 1 and 2 dimensions. 2.3. Levy flight. 2.4. Random walks with potentials. 2.5. Exercises. 3. Monte Carlo methods. 3.1. Objectives and concepts. 3.2. Monte-Carlo integration. 3.3. Markov Chain Monte-Carlo. 3.4. Advanced Error Analysis Techniques. 3.5. Error estimate in the presence of autocorrelation. 3.6. Error estimate for non-trivial estimators: The Jackknife, and the Bootstrap. 3.7. Biased Estimators. 3.8. Exercises. 4. Statistical models. 4.1. An introduction to thermodynamics. 4.2. From thermodynamics to statistical mechanics. 4.3. Phase transitions. 4.4. The Ising model. 4.5. An overview of other models. 4.6. Exercises. 5. Advanced Monte-Carlo simulation techniques. 5.1. Hamiltonian (Hybrid) Monte-Carlo (HMC) simulations. 5.2. Non-local Monte-Carlo update. 5.3. Micro-canonical simulations. 5.4. Flat histogram methods. 5.5. The Linear Logarithmic Relaxation (LLR) method. 5.6. Exercises. 6. From Statistical Systems to Quantum Field Theory. 6.1. Invitation: The O(2) model. 6.2. The Bridge to QFT: the Feynman path-integral. 6.3. Gauge Theories. 6.4. Adding fermion fields. 6.5. Exercises. 7. Current challenges in Monte-Carlo Simulations. 7.1. Sign and overlap problems. 7.2. Introduction to overlap problems. 7.3. Estimating probability density functions. 8. Data Analytics and Statistical Systems. 8.1. Model regression - L2 norm. 8.2. Gaussian Process. 8.3. Machine learning with graphs. 8.4. Emulation of statistical systems with Machine Learning. 8.5. Categorisation in statistical physics: Naive Bayes. 8.6. Machine learning classification of phase transitions.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
