From e549c84dd8ba368d5aa885e341c010ce4c0f3172 Mon Sep 17 00:00:00 2001 From: "github-actions[bot]" <41898282+github-actions[bot]@users.noreply.github.com> Date: Wed, 20 Nov 2024 09:29:35 +0000 Subject: [PATCH] Deploy Marp slides [skip ci] --- index.html | 399 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 399 insertions(+) create mode 100755 index.html diff --git a/index.html b/index.html new file mode 100755 index 0000000..07777fc --- /dev/null +++ b/index.html @@ -0,0 +1,399 @@ +
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24.10.2024
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Optimize your curves

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(No gym required)

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Oslo Python MeetUp

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Sunniva Indrehus

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📈 + 💪 + 🐍 = ❓

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sunniva@ngi$ echo $(whoami)
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Problem

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Optimization: an act, process, or methodology of making something (such as a design, system, or decision) as fully perfect, functional, or effective as possible
+specifically : the mathematical procedures (such as finding the maximum of a function) involved in this

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Curve Fitting: the empirical determination of a curve or function that approximates a set of data
+Merriam-Webster Dictionary

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A solution

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Another solution

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A third solution

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❗ Choose your model ❗

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Figure credit: PAGE, Ana M., et al. A macro-element pile foundation model for integrated analyses of monopile-based offshore wind turbines. Ocean Engineering, 2018, 167: 23-35.
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Real (NGI work) life example

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Figure credit: PAGE, Ana M., et al. A macro-element pile foundation model for integrated analyses of monopile-based offshore wind turbines. Ocean Engineering, 2018, 167: 23-35.
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Real (NGI work) life example

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+Horizontal displacement curves under load

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What is Curve Fitting?

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  • Find the best-fit curve for a dataset using a known model +
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    • Minimize the difference between observed and predicted values

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  • Categories of problems +
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    • Linear vs non-linear

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    • Unconstrained vs Constrained

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Difference between observed and predicted values

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Curve fitting requirements

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  • Estimate parameter uncertainties
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  • Support non-linear problem solving
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  • Easily change optimization algorithm
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  • Provide high-level tools for setting parameter bounds
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Recommended tool (by me)

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TopicDetails
Library Namelmfit
DescriptionHigh-level interface to non-linear optimization and curve fitting problems
GitHub Stars⭐ 1.1k
Last Commit Date13.10.2024 (on 22.10.2024)
Built OnSciPy’s curve_fit
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A new non-linear problem

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✨ Let's see some code ✨

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Problem setup

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from lmfit import Minimizer, create_params
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+def residual(parameters, x, data):
+    model = (
+        parameters["amplitude"]
+        * np.sin(x * parameters["omega"] + parameters["phi"])
+        * np.exp(-x * x * parameters["gamma"])
+    )
+    return model - data
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+parameters_initial = create_params(
+    amplitude=10,
+    gamma=0.1,
+    omega=3.0,
+    phi=0.0,
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+minimizer = Minimizer(residual, parameters_initial, fcn_args=(x, data))
+result = minimizer.minimize(method="least_squares")
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Handling bounds

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from lmfit import Parameters
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+params = Parameters()
+params.add('amplitude', value=10, min=0)
+params.add('gamma', value=0.1)
+params.add('phi', value=0.0, min=-np.pi/2., max=np.pi/2.)
+params.add('omega', value=3.0)
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from lmfit import create_params
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+params = create_params(amplitude=dict(value=10, min=0),
+                       gamma=0.1,
+                       omega=3,
+                       phi=dict(value=0, min=-np.pi/2, max=np.pi/2))
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Interpret simulation results

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[[Fit Statistics]]
+    # fitting method   = least_squares
+    # function evals   = 58
+    # data points      = 301
+    # variables        = 4
+    chi-square         = 12.1867036
+    reduced chi-square = 0.04103267
+    Akaike info crit   = -957.236198
+    Bayesian info crit = -942.407756
+[[Variables]]
+    amplitude:    5.03088066 +/- 0.04005821 (0.80%) (init = 10)
+    gamma:  0.02495457 +/- 4.5396e-04 (1.82%) (init = 0.1)
+    omega:  2.00026311 +/- 0.00326183 (0.16%) (init = 3)
+    phi: -0.10264955 +/- 0.01022294 (9.96%) (init = 0)
+[[Correlations]] (unreported correlations are < 0.100)
+    C(omega, phi) = -0.7852
+    C(amplitude, gamma)   = +0.5840
+    C(amplitude, phi)   = -0.1179
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📈 + 💪 + 🐍 = ❓

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📈 + 💪 + 🐍 = ❤️

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![w:450 h:350](figures/illustrations/scaled_pile_head_equal_beginning.png) +Horizontal displacement curves under load