Difference between revisions of "Team:ShanghaiTech/Software"

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         <h3>Function</h3>
 
         <h3>Function</h3>
 
         <p>Search proper parameter combinations for user-input parameterized differential equations so as to get the corresponding solution closer to a specified waveform.</p>
 
         <p>Search proper parameter combinations for user-input parameterized differential equations so as to get the corresponding solution closer to a specified waveform.</p>
−
         <p> <strong>Input</strong></p>
+
         <h3>Input</h3>
 
         <ol start='' >
 
         <ol start='' >
 
         <li>Parametrized Differential Equations</li>
 
         <li>Parametrized Differential Equations</li>
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         <h3>Description</h3>
 
         <h3>Description</h3>
 
         <p>As facing biodynamic modeling problems, we assumed that the hypersurface, which is formed by the parameterization of the L2-norm error between the parameter-corresponding solution and the desired waveform, is smooth and simple enough to reduce the high-dimensional optimization problems into simple maxi-searching problems. To be precise, we simplify the searching space from hyper-cubes into hyper-axises. The algorithm, which is a iteration, starts from a randomly chosen points in the allowed parameter space. By varying one parameter in the combination a time, we map the combinations into errors between the corresponding solutions and the desired waveform, from which we can find a ‘partial’ (in the sense of a ‘partial’ derivative) maxi on each axis. We compose those parameters as a whole combination and repeat the steps: varying each term at one time, finding ‘partially’ best parameters and compose until a satisfying error is achieved or the iteration limit has been met.</p>
 
         <p>As facing biodynamic modeling problems, we assumed that the hypersurface, which is formed by the parameterization of the L2-norm error between the parameter-corresponding solution and the desired waveform, is smooth and simple enough to reduce the high-dimensional optimization problems into simple maxi-searching problems. To be precise, we simplify the searching space from hyper-cubes into hyper-axises. The algorithm, which is a iteration, starts from a randomly chosen points in the allowed parameter space. By varying one parameter in the combination a time, we map the combinations into errors between the corresponding solutions and the desired waveform, from which we can find a ‘partial’ (in the sense of a ‘partial’ derivative) maxi on each axis. We compose those parameters as a whole combination and repeat the steps: varying each term at one time, finding ‘partially’ best parameters and compose until a satisfying error is achieved or the iteration limit has been met.</p>
 +
<h3>Manual</h3>
 +
  <ol start='' >
 +
        <li>At the welcome, you can choose the setting of this model. All parameter should be in Allowed Parameter Space. </li>
 +
        <li>Corresponding Solution</li>
 +
        <li>The Error of the Corresponding Solution from the Desired Waveform </li>
 +
 +
        </ol>
  
  

Revision as of 02:56, 18 October 2018

ShanghaiTech iGEM

Software

Meaning

Our software aims to help researchers to optimize their multi-parameterized differential dynamic systems for user-defined desired behaviors. It visualizes the error-vs.-parameter curves and highlights the local minimums, which can help users to integrate their direct sense into the parameter combination selection. Eventually, this software can combine users rich experience with the computation power from the machine to get rid of the boiler state in local random nonsense. On the other hand, the software provides a fully automatic working mode with optional configurable perturbation to reveal parts of the error-vs.-parameter hyper surface to help researchers on making their first guess. The backend API is also independently available in Matlab for general usage and further development in an open-source manner. The speed and precision of this toolkit has been validated on several typical biological dynamic systems and the outputs so far are acceptable and even satisfying.

Function

Search proper parameter combinations for user-input parameterized differential equations so as to get the corresponding solution closer to a specified waveform.

Input

  1. Parametrized Differential Equations
  2. Allowed Parameter Space
  3. Desired Solution
  4. (Optional) Maximum Iteration Count
  5. (Optional) Normalized Sampling Step

Output

  1. A Feasible Parameter Combination
  2. Corresponding Solution
  3. The Error of the Corresponding Solution from the Desired Waveform

Description

As facing biodynamic modeling problems, we assumed that the hypersurface, which is formed by the parameterization of the L2-norm error between the parameter-corresponding solution and the desired waveform, is smooth and simple enough to reduce the high-dimensional optimization problems into simple maxi-searching problems. To be precise, we simplify the searching space from hyper-cubes into hyper-axises. The algorithm, which is a iteration, starts from a randomly chosen points in the allowed parameter space. By varying one parameter in the combination a time, we map the combinations into errors between the corresponding solutions and the desired waveform, from which we can find a ‘partial’ (in the sense of a ‘partial’ derivative) maxi on each axis. We compose those parameters as a whole combination and repeat the steps: varying each term at one time, finding ‘partially’ best parameters and compose until a satisfying error is achieved or the iteration limit has been met.

Manual

  1. At the welcome, you can choose the setting of this model. All parameter should be in Allowed Parameter Space.
  2. Corresponding Solution
  3. The Error of the Corresponding Solution from the Desired Waveform

ShanghaiTech iGEM @ 2018