Machine learning approaches for solving nonlinear differential equations in sustainability science
*Monika KalraCorresponding authorMonikae6383@cumail.inDepartment of MathematicsChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Kiran Utrejakiran.e11227@cumail.inDepartment of MathematicsChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile → , Krishan KumarKrishan.e14313@cumail.inDepartment of Computer Science & EngineeringChandigarh UniversityMohali, Punjab, 140413, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2638
- Pages:
- 2519–2526
Abstract
Sustainability scientists often work with complex, nonlinear systems that are governed by differential equations. Traditional numerical methods are error-free, but when used in dynamic or uncertain environments, they can be rigid and computationally intensive. For approximating solutions to nonlinear differential equations (NLDEs), machine learning (ML), particularly deep learning, offers a versatile and data-driven framework. With an emphasis on sustainability applications, such as climate modeling, renewable energy systems, resource optimization, and environmental dynamics, this paper examines cuttingedge machine learning techniques applied to NLDEs. We show how operator learning techniques, Gaussian processes, and physics-informed neural networks (PINNs) can enhance computational efficiency and solution accuracy, underscoring their potential to facilitate sustainable decision-making in real time.
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References
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