.. _dynamic-solution:

================
Dynamic Solution
================

The NeurEco Dynamic solution creates neural network models for **time-series data** where inputs and outputs evolve over time. These models capture the temporal dynamics of systems, making them ideal for simulation, prediction, and digital twin applications.

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Overview
========

Dynamic models learn to predict how a system responds over time to changing inputs (excitations). Unlike static models that produce instantaneous outputs, dynamic models maintain internal state and produce trajectories that evolve according to learned dynamics.

**Key characteristics:**

- Models systems with memory (current output depends on past inputs/outputs)
- Handles variable-length time series
- Supports multiple experiments/sequences for training
- Exports to FMU format for simulation tool integration

When to Use Dynamic
===================

Choose the Dynamic solution when:

- Your data involves **time-dependent behavior**
- Outputs depend on the **history** of inputs, not just current values
- You're modeling **physical systems** (mechanical, thermal, electrical, etc.)
- You need to **simulate** system response to new input trajectories
- You want to create a **digital twin** of a real-world system

**Common applications:**

- Mechanical system simulation (vibrations, dynamics)
- Thermal modeling (heat transfer, temperature prediction)
- Control system design and testing
- Process modeling in manufacturing
- Environmental and climate modeling

Templates
=========

The Dynamic solution offers two templates for different types of temporal modeling:

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   * - Template
     - Best For
     - Key Features
   * - :ref:`ODE <ode-template>`
     - Systems governed by differential equations, physical systems with continuous dynamics
     - Learns hidden states, supports steady-state constraints, initialization from known conditions
   * - :ref:`Convolutional Dynamic <convolutive-template>`
     - Input-output relationships with time delays, signal processing, systems without explicit state
     - Sliding window approach, simpler architecture, faster training

Choosing Between ODE and Convolutional Dynamic
----------------------------------------------

**Choose ODE when:**

- The system has well-defined physical states (position, velocity, temperature, etc.)
- You need to initialize simulation from a known state
- The system has continuous dynamics governed by differential equations
- Long-term prediction accuracy is critical

**Choose Convolutional Dynamic when:**

- You're modeling input-output relationships with time delays
- The system behavior can be captured by a finite time window
- Training speed is a priority
- You don't need explicit state initialization

Data Requirements
=================

Dynamic models require time-series data organized as:

- **Time arrays**: Time stamps for each sample. **Convolutional Dynamic** requires uniformly spaced time steps; **ODE** only requires the time stamps to be sorted in strictly increasing order (the spacing may be non-uniform).
- **Excitation (input) arrays**: Input signals driving the system
- **Output arrays**: Target system responses

Multiple sequences (experiments) can be used for training. For Convolutional Dynamic they must share the same, uniform time step; for ODE the durations and the spacing may differ from one sequence to another.

See :ref:`dynamic-data-preparation` for detailed formatting requirements.

Native File Format
==================

Dynamic models use the ``.ernn`` extension for the native NeurEco format. This format:

- Preserves all model information
- Allows continued work in NeurEco
- Supports loading in the Python API
- Can be re-exported to FMU format

.. toctree::
   :maxdepth: 2
   :caption: Dynamic Solution

   data-preparation
   ode/index
   convolutive/index
   exporting
   advanced-features
   examples/index