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The paradigm shift to operator learning in physics-informed neural networks: A SciML review of DeepONet, FNO, and PINO Salsabila Endana Putri; Sherry Junira Sagita; Kheisya Nadiva Az-Zahra; Hamdi Akhsan; Nely Andriani
Gravity : Jurnal Ilmiah Penelitian dan Pembelajaran Fisika Vol 12, No 2 (2026)
Publisher : Universitas Sultan Ageng Tirtayasa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62870/gravity.v12i2.40359

Abstract

The transition from classical numerical methods which are often hampered by mesh dependency and the curse of dimensionality to Physics-Informed Neural Networks (PINNs) has marked a new paradigm shift in scientific computing through data-physics hybrid solutions. This study aims to map the evolutionary taxonomy of PINNs over the period from 2019 to 2024, with a specific focus on analysing the methodological transition from the Point-wise Prediction paradigm towards Operator Learning. Using a Focused Narrative Review approach on 36 selected primary studies, this review synthesises technological developments from the foundational phase to the latest architectural innovations. Key findings indicate that while standard PINNs offer mesh-free flexibility for single-equation instances, Neural Operator variants such as Deep Operator Networks (DeepONet) and Fourier Neural Operators (FNO) provide transformative computational efficiency. By adopting offline training and online inference strategies, these models are capable of achieving prediction speeds up to three orders of magnitude faster than traditional numerical solvers or standard PINNs. As a unique contribution, this article emphasises the urgency of a structured future research agenda, encompassing the pressing need for benchmark standardisation (such as the Scientific Machine Learning (SciML) initiative) and the development of architectural scalability to support exascale computing. This synthesis is intended to serve as a roadmap for the development of robust, industry-oriented digital twins.
Co-Authors Abidin Pasaribu Abidin Pasaribu Abidin Pasaribu, Abidin Adam Darmawan Ade Kurniawan Ade Kurniawan Agung Mataram Agung Sugiarto Agustina, Atika Ahmad Fauzi Ismail Ahmad Fudholi Aisyah Veronika Aji, Dwi Purnomo Aldi Prayoga Aljuzza, Muhammad Ikhsan Almafie, Muhammad Rama Amalia, Wardah Amanda Kurnia Utami Amanda Rahmannisa Andriani, Nelly Anggelina, Putri Anggelina, Zanne Anisa Qoriq Atun Nasiroh Apit Fathurohman Apit Fathurohman Arini Rosa Sinensis Atika Agustina Ayu Sekar Sari Azizah Putri Berimah Berimah, Azizah Putri Cahyani, Delvina Putri Cahyati, Nilam Damayanti, Fitria Siska Dani, Rahma Dea Amalia Dea Rizky Oktavia Dendi Juliansyah Deni Sadly Desilawati Detrika Mawar Arrum Devi Ardiantini Devi Ardiantini Dia Oktarina Gumanti Dwi Purnomo Aji Dwi Purnomo Aji Dwicahyani, Rania Dwita Kartika Sari Edo Anugrah Edray, Auliya Einsrizkianne Effendi Effendi Eka Sutinah Eka Sutinah Elsie Sulastry Erazando Alfa Seira Ermalia, Widia Evelina Astra Patriot Fahreza, Muhammad Aditya Fajriah, Nurkholisa Fatmawati, Fatmawati Fatonah, Amelia Febrianti, Tanti Fena Siska Putriyani Fernando Eric Redondo Fika Nurul Hidayati Fina Maliya Fitri Nisa Fitria Siska damayanti Fitria Siska Damayanti Fitriyani Fitriyani Guruh Sukarno Putra Hayati, Suci Husnul Huriyatul Firdausi I. Ismet Ida Sriyanti Iful Amri Iin Seprina Ina Agustina Intan Mahdiah Intan Purnama Sari Irenta Irenta Ishkaq Iskandar Iskhaq Iskandar Iskhaq Iskandar Iskhaq Iskandar Iskhaq Iskandar Isma Sari Ismet Ismet Ismet Ismet Ismet, Ismet Ismet, I. Izzah Nurhidayah, Izzah Jamiatul Khairunnisa Putri Jesi Pebralia Juwita Febrianti Kartika, Nadia Dwi Kayla Azzakia Ketang Wiyono Ketang Wiyono Ketang Wiyono Ketang Wiyono Kheisya Nadiva Az-Zahra KHOIRUN NISA Kiki Ayu Winarni Kistiono Kistiono Kistiono Kistiono Kistiono Kistiono Kistiono Kistiono Komarudin Komarudin Kurnia, Mega Lamura, M. Danny Pratama Lara Sania Laras Sapitri, Cindy Leni Marlina Leni Marlina Leni Marlina Lestari, Mutiah Lestari, Yora Inda Lira Diska Wati Lira Lira Lira, Lira Lismayana, Pegi Putri M. Nicola Prajaska Maghfira Aulia Mahdiah, Intan Mahmudah, Indri Markos Siahaan, Sardianto Masduki Masduki Mega Kurnia Mega Kurnia Meilanie, Trista Meliani Devina Melinda Maharani Melly Ariska Melly Ariska Melly Junita Melvany, Nanda Eva Miftahul Jannah Mindia Vanessa Pratiwi, Sri Muhamad Yusup Muhamad Yusup Muhamad Yusup Muhammad Aditiyah Muhammad Afrizal Muhammad afrizal Muhammad Aufa Riyaldo Muhammad Irfan Muhammad Irfan Muhammad Irfan Muhammad Irfan Muhammad Irfan muhammad muslim Muhammad Muslim Muhammad Muslim Muhammad Muslim, Muhammad Muhammad Romadoni Muhammad Romadoni Muhammad Yusuf Muhammad Yusup Murnia Murniati Murniati . Mutia Faradini Ramadhanty Mutiah Lestari Mutiara Putri Nadiah Alfania Nadiar Pertiwi Nadya Anggraini Nadya Anggraini Nasiroh, Anisa Qoriq Atun Nazhifah, Rizqia Nely Andriani Nely andriani Nely Andriani, Nely Nestity, Alifia Nia Nopeliza, Nia Nia Three Manurung Nia Three Manurung Nia Three Manurung Nilam Cahyati Nita Arrum Sari Noor Dayana Abd Halim Nor Farahwahidah Abdul Rahman Nor Farahwahidah Abdul Rahman Nora Herliza Noviana, RA Sania Nur Kayla Lekati Nurkholisa Fajriah Pertiwi, Nadiar Pratiwi Ineke Anwar Putra, Gede Mudita Edi Putra, Guruh Sukarno Putri Anggelina Putri Maulida, Nabila Putri Nurhikmah Putri Wijayanti Putri, Arselly Rahmanda Putri, Jamiatul Khairunnisa Putri, Mutiara Juliana Putriyani, Fena Siska Qathrunnada, Sausan Rahma Hafitri Rahman, Nor Farahwahidah Abdul Rahmannisa, Amanda Ramadhani, Neysya Ditha Ramadhona, Tyse Rara Rara Resta Ulis Muslimah Ribkoh, Ribkoh Risa Albeta Rita Inderawati Rizki Novianti, Rizki Romadoni, Muhammad Rosada, Mita Rosdiana Salmah Rianti Salmah Rianti Salsa bila Salsabila Endana Putri Salsabillah, Zahwa Nur Saparini Saparini Sardianto Markos Siahaan Sardianto Markos Siahaan Sardianto Markos Siahaan Sardianto Markos Siahaan, Sardianto Markos Sari, Dwita Kartika Sari, Mona Sekarani, Tresnane Suandti Selvia Mariska Syahputri Seprina, Iin Sherry Junira Sagita Sholeha, Nurlita Dwi Siti Kurdiah Siti Nur Azizah Sopia Sopia Sri Mindia Vanessa Pratiwi Sri Zakiyah Sudirman Sudirman Sudirman Sudirman Suhadi Suhadi Suhadi Suhadi Suhadi Sunarti, Arinda Rahma Supardi Supardi Supardi Supari Supari Supari Supari Supari Supari Supari, Supari Sutanto, Taufiq Syahputri, Selvia Mariska Syahrani, Revanola Gusti Syuhendri, Syuhendri Tamara Shelvy Maharani Tanti Febrianti Taufiq Sutanto Taufiq Taufiq Taufiq Taufiq Tina Oktasari Tine Aprianti Tita Ratna Wulan Dari Tresnane Suandti Sekarani Trista Meilanie Tsabita Husna Tyse Ramadhona Utami, Amanda Kurnia Vania, Amanda Asti VIOLANTI ANARKY, VIOLANTI Wahyuningsi, Wahyuningsi Wailaina Wardah Amalia Wati, Lira Diska Winarni, Kiki Ayu Yendri Tri Hartati Napitupulu Yenny Anwar Yesi Monalika Yuli Setianingsih Yuliana, Rahma Zahlia, Marsela Zahra Ayanna Firmansyah Zahrani, Ami Zulherman Zulherman Zulherman Zulherman, Zulherman