Computational Geosciences

  1. Data-Driven Methods and Machine Learning
    1. Inverse Problems and Parameter Estimation
      1. Theory of Inverse Problems
        1. Well-posed vs. Ill-posed Problems
          1. Existence
            1. Uniqueness
              1. Stability
              2. Forward and Inverse Modeling
                1. Forward Operators
                  1. Inverse Operators
                    1. Model Parameterization
                  2. Regularization Techniques
                    1. Tikhonov Regularization
                      1. L2 Regularization
                        1. Parameter Selection
                          1. Generalized Cross-Validation
                          2. Sparsity-Promoting Methods
                            1. L1 Regularization
                              1. Total Variation
                                1. Compressed Sensing
                              2. Markov Chain Monte Carlo Methods
                                1. Metropolis-Hastings Algorithm
                                  1. Proposal Distributions
                                    1. Acceptance Criteria
                                      1. Convergence Diagnostics
                                      2. Gibbs Sampling
                                        1. Conditional Distributions
                                          1. Block Sampling
                                            1. Convergence Assessment
                                        2. Data Assimilation
                                          1. Variational Methods
                                            1. 3D-Var
                                              1. Cost Function
                                                1. Background Error Covariance
                                                  1. Observation Error Covariance
                                                  2. 4D-Var
                                                    1. Time Window
                                                      1. Adjoint Models
                                                        1. Incremental Approach
                                                      2. Sequential Methods
                                                        1. Kalman Filter
                                                          1. Linear Systems
                                                            1. Optimal Estimation
                                                              1. Error Propagation
                                                              2. Ensemble Kalman Filter
                                                                1. Ensemble Generation
                                                                  1. Covariance Estimation
                                                                    1. Localization Techniques
                                                                  2. Combining Observational Data with Models
                                                                    1. Observation Operators
                                                                      1. Linear Operators
                                                                        1. Nonlinear Operators
                                                                          1. Tangent Linear Models
                                                                          2. Error Covariance Estimation
                                                                            1. Background Errors
                                                                              1. Observation Errors
                                                                                1. Model Errors
                                                                            2. Machine Learning Applications in Geosciences
                                                                              1. Supervised Learning
                                                                                1. Classification
                                                                                  1. Land Cover Classification
                                                                                    1. Remote Sensing Data
                                                                                      1. Feature Extraction
                                                                                        1. Accuracy Assessment
                                                                                        2. Seismic Facies Classification
                                                                                          1. Seismic Attributes
                                                                                            1. Pattern Recognition
                                                                                              1. Geological Interpretation
                                                                                            2. Regression
                                                                                              1. Predicting Material Properties
                                                                                                1. Rock Properties
                                                                                                  1. Soil Characteristics
                                                                                                    1. Fluid Properties
                                                                                                    2. Environmental Variable Estimation
                                                                                                      1. Temperature Prediction
                                                                                                        1. Precipitation Estimation
                                                                                                          1. Air Quality Modeling
                                                                                                      2. Unsupervised Learning
                                                                                                        1. Clustering
                                                                                                          1. Identifying Climate Patterns
                                                                                                            1. Weather Regimes
                                                                                                              1. Climate Modes
                                                                                                                1. Extreme Events
                                                                                                                2. Grouping Geophysical Signals
                                                                                                                  1. Seismic Event Classification
                                                                                                                    1. Electromagnetic Anomalies
                                                                                                                      1. Gravity Patterns
                                                                                                                    2. Dimensionality Reduction
                                                                                                                      1. Principal Component Analysis
                                                                                                                        1. Eigenvalue Decomposition
                                                                                                                          1. Variance Explanation
                                                                                                                            1. Data Compression
                                                                                                                            2. t-Distributed Stochastic Neighbor Embedding
                                                                                                                              1. Nonlinear Mapping
                                                                                                                                1. Perplexity Parameter
                                                                                                                                  1. Visualization Applications
                                                                                                                              2. Deep Learning
                                                                                                                                1. Convolutional Neural Networks for Image and Gridded Data
                                                                                                                                  1. Image Segmentation
                                                                                                                                    1. Semantic Segmentation
                                                                                                                                      1. Instance Segmentation
                                                                                                                                        1. Medical Imaging
                                                                                                                                        2. Feature Extraction
                                                                                                                                          1. Convolutional Layers
                                                                                                                                            1. Pooling Layers
                                                                                                                                              1. Transfer Learning
                                                                                                                                            2. Recurrent Neural Networks for Time-Series Data
                                                                                                                                              1. Sequence Modeling
                                                                                                                                                1. LSTM Networks
                                                                                                                                                  1. GRU Networks
                                                                                                                                                    1. Attention Mechanisms
                                                                                                                                                    2. Forecasting Applications
                                                                                                                                                      1. Weather Prediction
                                                                                                                                                        1. Climate Projections
                                                                                                                                                          1. Hydrological Forecasting
                                                                                                                                                        2. Physics-Informed Neural Networks
                                                                                                                                                          1. Incorporating Physical Laws
                                                                                                                                                            1. Differential Equations
                                                                                                                                                              1. Conservation Laws
                                                                                                                                                                1. Boundary Conditions
                                                                                                                                                                2. Applications in Forward and Inverse Problems
                                                                                                                                                                  1. Parameter Estimation
                                                                                                                                                                    1. Model Discovery
                                                                                                                                                                      1. Uncertainty Quantification

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                                                                                                                                                              6. Modeling of Fluid Earth Systems

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                                                                                                                                                              8. Software Development and Model Validation