AI Feynman: A physics-inspired method for symbolic regression

Udrescu, Silviu-Marian; Tegmark, Max

doi:10.1126/sciadv.aay2631

Cited by 608 publications

(387 citation statements)

References 30 publications

Supporting

Mentioning

381

Contrasting

Unclassified

Order By: Relevance

“…In AI, there are many attempts to build symbolic regression algorithms, which are automated tools to find the mathematical equation that fits the experimental data [33]. Udrescu and Tegmark [34] developed an algorithm that combines neural network fitting with a set of physics-inspired techniques. They applied it to 100 equations from the Feynman lectures on physics.…”

Section: Proposed Frameworkmentioning

confidence: 99%

Artificial General Intelligence: A New Perspective, with Application to Scientific Discovery

Khalili¹

2022

Preprint

View full text Add to dashboard Cite

The dream of building machines that have human-level intelligence has inspired scientists for decades. Remarkable advances have been made recently; however, we are still far from achieving this goal. In this paper, I propose an alternative perspective on how these machines might be built focusing on the scientific discovery process which represents one of our highest abilities that requires a high level of reasoning and remarkable problem-solving ability. By trying to replicate the procedures followed by many scientists, the basic idea of the proposed approach is to use a set of principles to solve problems and discover new knowledge. These principles are extracted from different historical examples of scientific discoveries. Building machines that fully incorporate these principles in an automated way might open the doors for many advancements.

show abstract

Section: Proposed Frameworkmentioning

confidence: 99%

Artificial General Intelligence: A New Perspective, with Application to Scientific Discovery

Khalili¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…It has been shown that a good design of the search space is essential in discrete structure optimization problems, e.g., neural architecture search [10][11][12], molecule optimization [13], composite design [14] and symbolic regression [15,16]. Since the QAOA is a well-recognized ansatz for combinatorial problems, we have designed the search space for G A based on gradual modifications of the QAOA ansatz.…”

Section: A Ansatz Architecture Searchmentioning

confidence: 99%

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

Fan

Coram

et al. 2020

Phys. Rev. Research

107

View full text Add to dashboard Cite

The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a prescription for choosing the variational parameters of the circuit. We propose modifications to both. First, we define the Gibbs objective function and show that it is superior to the energy expectation value for use as an objective function in tuning the variational parameters. Second, we describe an Ansatz Architecture Search (AAS) algorithm for searching the discrete space of quantum circuit architectures near the QAOA to find a better ansatz. Through the AAS we find quantum circuits with the same number of variational parameters as the QAOA but which have improved performance on certain Ising-type problems. This opens a new research field of quantum circuit architecture design for quantum optimization algorithms.arXiv:1909.07621v1 [quant-ph]

show abstract

“…However, the functional form of H is usually unknown a priori. Although there are some methods proposed in the literature to identify functional forms from the data, inferring functional forms usually requires a large amount of data and can be computationally expensive [49][50][51][52][53][54]. Instead, we assume H to be an ANN model.…”

Section: Development Of Artificial Neural Network Modelsmentioning

confidence: 99%

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

2020

View full text Add to dashboard Cite

Developing an accurate first-principle model is an important step in employing systems biology approaches to analyze an intracellular signaling pathway. However, an accurate first-principle model is difficult to be developed since it requires in-depth mechanistic understandings of the signaling pathway. Since underlying mechanisms such as the reaction network structure are not fully understood, significant discrepancy exists between predicted and actual signaling dynamics. Motivated by these considerations, this work proposes a hybrid modeling approach that combines a first-principle model and an artificial neural network (ANN) model so that predictions of the hybrid model surpass those of the original model. First, the proposed approach determines an optimal subset of model states whose dynamics should be corrected by the ANN by examining the correlation between each state and outputs through relative order. Second, an L2-regularized least-squares problem is solved to infer values of the correction terms that are necessary to minimize the discrepancy between the model predictions and available measurements. Third, an ANN is developed to generalize relationships between the values of the correction terms and the system dynamics. Lastly, the original first-principle model is coupled with the developed ANN to finalize the hybrid model development so that the model will possess generalized prediction capabilities while retaining the model interpretability. We have successfully validated the proposed methodology with two case studies, simplified apoptosis and lipopolysaccharide-induced NFκB signaling pathways, to develop hybrid models with in silico and in vitro measurements, respectively.

show abstract

AI Feynman: A physics-inspired method for symbolic regression

Cited by 608 publications

References 30 publications

Artificial General Intelligence: A New Perspective, with Application to Scientific Discovery

Artificial General Intelligence: A New Perspective, with Application to Scientific Discovery

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

Development of a hybrid model for a partially known intracellular signaling pathway through correction term estimation and neural network modeling

Contact Info

Product

Resources

About