surrogates

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   - caption: numpyro
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       - file: chapters/numpyro/introduction
+      - file: chapters/numpyro/surrogates

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+# Surrogate Models in Astronomy: Why and How with Python and JAX
+
+Surrogate models, also known as metamodels or emulator models, are simplified representations of more complex models. They are used in various fields, including astronomy, to make predictions about a system without having to run a full simulation, which can be computationally expensive and time-consuming.
+
+## Why Surrogate Models?
+
+In astronomy, simulations of planets, stars, galaxies or the Universe and phenomena can involve complex physics and large datasets, making them computationally intensive. Surrogate models provide a way to approximate these simulations, offering several advantages:
+
+1. **Efficiency**: Surrogate models are faster to run than full simulations, making them useful for tasks that require many iterations, such as parameter tuning or uncertainty quantification.
+2. **Interpretability**: Surrogate models can be easier to interpret than the original models, helping to understand the underlying physics.
+3. **Feasibility**: In some cases, running a full simulation may not be feasible due to resource constraints. Surrogate models provide a viable alternative.
+
+## How to Create Surrogate Models with Python and JAX
+
+Python, a high-level programming language, is widely used in astronomy for its readability and extensive scientific libraries. JAX, a Python library, extends the capabilities of NumPy and autograd to leverage hardware accelerators like GPUs or TPUs.
+
+Here's a simplified process of creating a surrogate model:
+
+1. **Data Preparation**: Gather data from the original model or simulation. This could be a set of input parameters and corresponding outputs.
+2. **Model Training**: Use a machine learning algorithm to train a model on this data. JAX can be used for this step, as it provides automatic differentiation and XLA-compiled machine learning routines.
+3. **Model Validation**: Validate the surrogate model against the original model or simulation. This could involve comparing the outputs of the surrogate model with those of the original model for a new set of inputs.
+
+## Limitations of Surrogate Models
+
+While surrogate models offer many advantages, they also have limitations:
+
+1. **Accuracy**: Surrogate models are approximations, so they may not capture all the nuances of the original model or simulation.
+2. **Overfitting**: If the surrogate model is too complex or the training data is too sparse, the model may overfit to the training data and perform poorly on new data.
+3. **Extrapolation**: Surrogate models are based on the data they were trained on and may not perform well when extrapolating beyond this data.
+
+Despite these limitations, surrogate models remain a powerful tool in astronomy, enabling researchers to make predictions and gain insights more efficiently.