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Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning

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ANFIS from scratch with Python: five layers, hybrid least squares and gradient descent learning, forecasting. Episode 3 of the ANFIS metaheuristics time series forecasting series.

Software: Python (NumPy, statsmodels, PyTorch, Matplotlib)
Level: Advanced
Duration: ± 12 min
Series total: 59 min · 6 videos
Published: October 25, 2026

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Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Cover: Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning

Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Before you start, steps list, and Step 1

Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Step 2: Hybrid learning

Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Step 3: Training on two series

Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Step 4: Forecasting & Membership Function

Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning: Done: Final Result and Further Practice

Cover: Class ANFIS Metaheuristics Time Series Forecasting #3: Building ANFIS from Scratch: Five Layers and Hybrid Learning

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Transcript

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Introduction

Here is the final result, Anvis that we wrote from scratch, learning from data with hybrid learning. The 6-step Mackey-Glass forecast almost perfectly overlaps with the original, with an error of only 0.3%. We also found the overfitting trap on sunspots and how to overcome it. Let's start. Hello, welcome to episode three of the Anvis Metaheuristics series for time series forecasting. Anvis, Adaptive Neurofuzzy Inference System, was introduced in the early 1990s. Its structure is the same as the Sugeno system, but its parameters are trained like a neural network. The key is the highly efficient hybrid learning. Today we are writing it.

Step 1: ANFIS Layers & Least Squares

Create a file anvis.py With 4 inputs and 2 membership functions per input, there are 2 to the power of 4, which is 16 rules. Premise parameters are the center and width of the Gaussian, 16 numbers, and consequent parameters 5 numbers per rule, totaling 80. The forward function calculates layers 1 to 3 along with the output. The consequent function is half of the hybrid learning. With fixed premises, the Anvis output is linear to the consequent, so the optimal value is obtained in one least squares calculation. The lay function adds ridge regularization so that coefficients do not grow excessively. The train function runs the hybrid learning.

Step 2: Hybrid Learning

Each epoch, the consequent is calculated with least squares, then the error is backpropagated through the normalization layer and rule strength to calculate the gradients of the center and width of each membership function, and both are updated with gradient descent. The premise and rule premise functions convert premise parameters into a vector, which is later used by the metaheuristic algorithm. Create a file train_underscore_anvis.py and run it.

Step 3: Training on Two Series

We also trained the version without ridge as a comparison. On Mackey Glass, Anvis achieves RMSI train 0.0025 and test 0.0032 in 1 second. On Sunspot, RMSI test 0.1265, but without ridge RMSI test explodes to 2.02. The reason is that the test Sunspot data contains higher peaks than the train data, and 80 coefficients without constraints extrapolate wildly. Regularization tames it.

Step 4: Forecasting & Membership Functions

Let's see the graph. RMSI train drops during 100 epochs. Forecast Mackey Glass, dashed line, almost indistinguishable from actual data, whereas the Sunspot forecast follows the cycle but misses some peaks. The right panel shows the membership functions shifting from initial points to new positions learned from the data.

Done!

Done. We have built Anvis from 0 with 5 layers, least squares with ridge regularization, and gradient descent, and trained it on 2 time series. In the next episode, we will optimize the premise parameters with PSO and genetic algorithms. Currently working on a thesis, dissertation, or research in the field of forecasting and artificial intelligence. Cerdas Inovasi Digital helps implement forecasting models, from Sugeno fuzzy systems and Anvis, parameter optimization with PSO and genetic algorithms, up to LSTM and ARIMA comparisons and Diebold Mariano tests, as well as opening Python programming courses for engineering. Want to master the entire series, from chaotic time series to statistical evaluation? All 6 episodes, complete with step-by-step PDF guides, data sets, and source code, are available for premium tutorial subscribers. Subscribe starting at Rp69.000 per month, save 28% with the 12-month package, or pay once Rp999.000 for lifetime access. Thank you for watching, see you in the next episode. Thank you for watching,

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Transcript

0:03Introduction

0:51Step 1: ANFIS Layers & Least Squares

4:40Step 2: Hybrid Learning

6:57Step 3: Training on Two Series

8:50Step 4: Forecasting & Membership Functions

10:51Done!

Ask the class material

My notes

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▶ Video Lesson

Recommended classes for you

Need more than a video?

Transcript

0:03Introduction

0:51Step 1: ANFIS Layers & Least Squares

4:40Step 2: Hybrid Learning

6:57Step 3: Training on Two Series

8:50Step 4: Forecasting & Membership Functions

10:51Done!

Ask the class material

My notes

Questions & answers

Your instructor

Introduction

Step 1: ANFIS Layers & Least Squares

Step 2: Hybrid Learning

Step 3: Training on Two Series

Step 4: Forecasting & Membership Functions

Done!

Introduction

Step 1: ANFIS Layers & Least Squares

Step 2: Hybrid Learning

Step 3: Training on Two Series

Step 4: Forecasting & Membership Functions

Done!