Tyler Ray Josephson
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Tyler Ray Josephson has a total of 84 co-authors. Here are the top co-authors by number of shared publications:
- Joern Ilja Siepmann
Department of Chemical Engineering and Materials Science University of Minnesota Minneapolis Minnesota USA
7 shared publications - Stavros Caratzoulas
Delaware Energy Institute, University of Delaware, Newark, Delaware 19716, United States
5 shared publications - Dionisios G. Vlachos
Department of Chemical and Biomolecular Engineering, University of Delaware, 150 Academy St., Newark, DE 19716, USA
4 shared publications Dionisios G. Vlachos
3 shared publicationsGeorge Tsilomelekis
Catalysis Center for Energy Innovation, Department of Chemical and Biomolecular Engineering, University of Delaware, 150 Academy Street, Newark, Delaware 19716, United States
3 shared publicationsSamiha Sharlin
Department of Chemical, Biochemical & Environmental Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250, United States
3 shared publications
Latest Publications
- Open Access
- 26 October 2026
- Published by Wiley in ChemCatChem
- Vol. 18 (20)
Role of Alcohol Solvents in Glucose Isomerization and Etherification in Modulated UiO‐66
Solvent choice significantly affects the rates of glucose isomerization and its selectivity to fructose. Glucose isomerization was examined over modulated UiO‐66(Zr) in methanol and 1‐propanol solvents. Reactions in 1‐propanol favor glucose isomerization to fructose, whereas reactions in methanol favor glucose etherification side reactions to glucosides, which reduces fructose selectivity. The fructose that forms subsequently reacts with both propanol and methanol solvents to form fructosides. Density functional theory calculations examine the key reactions and the important role of solvation in affecting fructose selectivity. The higher hydrogen‐bonding acidity provided by the methanol solvation environment, as compared to 1‐propanol, stabilizes transition states involving the alkoxide attack on glucose in the etherification pathway. Methanol molecules form a more intimate hydrogen‐bonding network thus stabilizing anionic intermediates during reaction. As such, methanol, which is more acidic than propanol, enhances alkoxide‐mediated etherification relative to Lewis‐acid‐catalyzed isomerization. Experiments carried out in mixtures of these alcohols show that methanol‐rich environments favor glucose etherification (over isomerization), in contrast to 1‐propanol‐rich environments favor isomerization. Notably, the calculated free energy differences between isomerization and etherification (+1.0 kcal/mol in methanol and –3.9 kcal/mol in 1‐propanol) are consistent with those from kinetic experiments (0.3 kcal/mol in methanol and −2.2 kcal/mol in propanol).
- 26 October 2026
- Published by Wiley in ChemCatChem
- Vol. 18 (20)
Open AccessRole of Alcohol Solvents in Glucose Isomerization and Etherification in Modulated UiO‐66
Solvent choice significantly affects the rates of glucose isomerization and its selectivity to fructose. Glucose isomerization was examined over modulated UiO‐66(Zr) in methanol and 1‐propanol solvents. Reactions in 1‐propanol favor glucose isomerization to fructose, whereas reactions in methanol favor glucose etherification side reactions to glucosides, which reduces fructose selectivity. The fructose that forms subsequently reacts with both propanol and methanol solvents to form fructosides. Density functional theory calculations examine the key reactions and the important role of solvation in affecting fructose selectivity. The higher hydrogen‐bonding acidity provided by the methanol solvation environment, as compared to 1‐propanol, stabilizes transition states involving the alkoxide attack on glucose in the etherification pathway. Methanol molecules form a more intimate hydrogen‐bonding network thus stabilizing anionic intermediates during reaction. As such, methanol, which is more acidic than propanol, enhances alkoxide‐mediated etherification relative to Lewis‐acid‐catalyzed isomerization. Experiments carried out in mixtures of these alcohols show that methanol‐rich environments favor glucose etherification (over isomerization), in contrast to 1‐propanol‐rich environments favor isomerization. Notably, the calculated free energy differences between isomerization and etherification (+1.0 kcal/mol in methanol and –3.9 kcal/mol in 1‐propanol) are consistent with those from kinetic experiments (0.3 kcal/mol in methanol and −2.2 kcal/mol in propanol).
- 21 May 2026
- Published by American Chemical Society (ACS) in Journal of Chemical Information and Modeling
- Vol. 66 (11) , 6299-6312
NMR-Challenge for LLMs: Evaluating Chemical Reasoning in Humans and AI
Nuclear magnetic resonance (NMR) structure determination is an important problem in education, industry, and research. Solving NMR spectra requires expert knowledge, critical thinking, and careful evaluation of multiple features of spectral data. This study explores the capabilities of large language models (LLMs) and large reasoning models (LRMs) for solving NMR spectral tasks. We selected 112 problems from NMR-Challenge.com, which has been used by students practicing NMR structure elucidation, collecting >1 million human responses, and developed a plain text problem format for evaluating LLM reasoning in this domain. We evaluated 10 LLMs (GPT-4o, GPT-4o-mini, o1, o1 mini, o3 mini, Claude-3.5 Sonnet, Gemini 2.0 Flash, Meta Llama 3, ChemDFM-R, and ether0), comparing 5 prompts to spur chain-of-thought reasoning in different ways, especially comparing the influence of providing background NMR chemistry knowledge, reasoning strategy, or both. Newer models trained to emphasize reasoning performed better, and increasing reasoning effort led to modest improvements, but prompting and varying temperature did not have an effect. We also evaluated undergraduate organic chemistry students in a controlled setting and analyzed answer submission statistics from global submissions to NMR-Challenge.com, to characterize human performance on these problems. The top-performing students surpassed smaller models like GPT-4o by 24%, 33%, and 29% on the Easy, Moderate, and Hard sets, respectively. However, reasoning models like o1 exceeded student performance by 13%, 14%, and 19%, respectively. Patterns in mistakes made by humans and LLMs reveal that errors made by LLMs are similar to those typically made by humans, for instance, incorrect positioning of substituents on benzene and incorrect orientation of carboxyl groups in esters. However, LLMs still “think” differently from humans, in some cases, providing answers that no human submitted via the website. This work also illustrates how NMR spectral problems can be used to benchmark LLMs on reasoning-heavy tasks in chemistry, though for this particular set of problems, early 2025 LLMs already exceed undergraduate student performance.
- 21 May 2026
- Published by American Chemical Society (ACS) in Journal of Chemical Information and Modeling
- Vol. 66 (11) , 6299-6312
NMR-Challenge for LLMs: Evaluating Chemical Reasoning in Humans and AI
Nuclear magnetic resonance (NMR) structure determination is an important problem in education, industry, and research. Solving NMR spectra requires expert knowledge, critical thinking, and careful evaluation of multiple features of spectral data. This study explores the capabilities of large language models (LLMs) and large reasoning models (LRMs) for solving NMR spectral tasks. We selected 112 problems from NMR-Challenge.com, which has been used by students practicing NMR structure elucidation, collecting >1 million human responses, and developed a plain text problem format for evaluating LLM reasoning in this domain. We evaluated 10 LLMs (GPT-4o, GPT-4o-mini, o1, o1 mini, o3 mini, Claude-3.5 Sonnet, Gemini 2.0 Flash, Meta Llama 3, ChemDFM-R, and ether0), comparing 5 prompts to spur chain-of-thought reasoning in different ways, especially comparing the influence of providing background NMR chemistry knowledge, reasoning strategy, or both. Newer models trained to emphasize reasoning performed better, and increasing reasoning effort led to modest improvements, but prompting and varying temperature did not have an effect. We also evaluated undergraduate organic chemistry students in a controlled setting and analyzed answer submission statistics from global submissions to NMR-Challenge.com, to characterize human performance on these problems. The top-performing students surpassed smaller models like GPT-4o by 24%, 33%, and 29% on the Easy, Moderate, and Hard sets, respectively. However, reasoning models like o1 exceeded student performance by 13%, 14%, and 19%, respectively. Patterns in mistakes made by humans and LLMs reveal that errors made by LLMs are similar to those typically made by humans, for instance, incorrect positioning of substituents on benzene and incorrect orientation of carboxyl groups in esters. However, LLMs still “think” differently from humans, in some cases, providing answers that no human submitted via the website. This work also illustrates how NMR spectral problems can be used to benchmark LLMs on reasoning-heavy tasks in chemistry, though for this particular set of problems, early 2025 LLMs already exceed undergraduate student performance.
- Open Access
- 8 September 2025
- Published by American Chemical Society (ACS) in ChemRxiv
Automating Reasoning in Chemical Science and Engineering
Step-by-step thinking is essential in all domains of chemical sciences and engineering. While machine learning tools are broadly used, algorithms that automate reasoning are far less common. We elaborate on seven categories of human reasoning activities and connect each to applications in chemical science and engineering: inductive, deductive, abductive, probabilistic, causal, analogical, and informal reasoning. For each, we describe approaches and tools for implementing in computational settings. We find the traditional categories of logic (induction, deduction, abduction) to be useful for interpreting a wide range of research activities in the computational sciences: curve fitting and supervised learning are induction, predicting from a curve or a supervised model is deduction, first-principles simulations are deduction, molecular structure elucidation is abduction, and inverse design is isomorphic to abduction. Experimental design incorporates themes of all three, but also stands apart because it modifies the data. We also survey the ``reasoning'' capabilities of large language models, and illustrate some challenges and opportunities in building systems that learn to reason. Central concepts that emerge include the dual nature of reasoning as propositional and step-by-step (the "what" and the "how"), the importance of appreciating syntax and semantics, and the centrality of abstraction in formal and informal contexts. Throughout, we highlight untapped opportunities, including bug-free scientific computing software, predictive modeling approaches to generalize outside training data, inverse design, and automated hypothesis generation and evaluation.
- 8 September 2025
- Published by American Chemical Society (ACS) in ChemRxiv
Open AccessAutomating Reasoning in Chemical Science and Engineering
Step-by-step thinking is essential in all domains of chemical sciences and engineering. While machine learning tools are broadly used, algorithms that automate reasoning are far less common. We elaborate on seven categories of human reasoning activities and connect each to applications in chemical science and engineering: inductive, deductive, abductive, probabilistic, causal, analogical, and informal reasoning. For each, we describe approaches and tools for implementing in computational settings. We find the traditional categories of logic (induction, deduction, abduction) to be useful for interpreting a wide range of research activities in the computational sciences: curve fitting and supervised learning are induction, predicting from a curve or a supervised model is deduction, first-principles simulations are deduction, molecular structure elucidation is abduction, and inverse design is isomorphic to abduction. Experimental design incorporates themes of all three, but also stands apart because it modifies the data. We also survey the ``reasoning'' capabilities of large language models, and illustrate some challenges and opportunities in building systems that learn to reason. Central concepts that emerge include the dual nature of reasoning as propositional and step-by-step (the "what" and the "how"), the importance of appreciating syntax and semantics, and the centrality of abstraction in formal and informal contexts. Throughout, we highlight untapped opportunities, including bug-free scientific computing software, predictive modeling approaches to generalize outside training data, inverse design, and automated hypothesis generation and evaluation.
- Open Access
- 13 August 2025
- Published by American Chemical Society (ACS) in ChemRxiv
NMR-Challenge for LLMs: Evaluating Chemical Reasoning in Humans and AI
Nuclear Magnetic Resonance (NMR) structure determination is an important problem in education, industry, and research. Solving NMR spectra requires expert knowledge, critical thinking, and careful evaluation of multiple features of spectral data. This study explores the capabilities of large language models (LLMs) for solving NMR spectral tasks. We selected 115 problems from NMR-Challenge.com, which has been used by students practicing NMR structure elucidation, collecting >1 million human responses, and developed a plain text problem format for evaluating LLM reasoning in this domain. We evaluated 7 LLMs (GPT-4o, GPT-4o-mini, o1, o1-mini, o3-mini, Claude-3.5 Sonnet, and Gemini-2.0-Flash), comparing 5 prompts to spur chain-of-thought reasoning in different ways, especially comparing the influence of providing background NMR chemistry knowledge, reasoning strategy, or both. Newer models trained to emphasize reasoning performed better, and increasing reasoning effort led to modest improvements, but prompting and varying temperature didn't have an effect. We also evaluated undergraduate organic chemistry students in a controlled setting, and analyzed answer submission statistics from global submissions to NMR-Challenge.com, to characterize human performance on these problems. The top-performing students surpassed smaller models like GPT-4o by 24%, 33%, and 29% on the Easy, Moderate, and Hard sets. However, reasoning models like o1 exceeded student performance by 13%, 14%, and 19%, respectively. Patterns in mistakes made by humans and LLMs reveal that errors made by LLMs are similar to those typically made by humans, for instance, incorrect positioning of substituents on benzene and incorrect orientation of carboxyl groups in esters. However, LLMs still "think" differently from humans, in some cases, providing answers which no human submitted via the website. This work also illustrates how NMR spectral problems can be used to benchmark LLMs on reasoning-heavy tasks in chemistry, though for this particular set of problems, current LLMs already exceed undergraduate student performance.
- 13 August 2025
- Published by American Chemical Society (ACS) in ChemRxiv
Open AccessNMR-Challenge for LLMs: Evaluating Chemical Reasoning in Humans and AI
Nuclear Magnetic Resonance (NMR) structure determination is an important problem in education, industry, and research. Solving NMR spectra requires expert knowledge, critical thinking, and careful evaluation of multiple features of spectral data. This study explores the capabilities of large language models (LLMs) for solving NMR spectral tasks. We selected 115 problems from NMR-Challenge.com, which has been used by students practicing NMR structure elucidation, collecting >1 million human responses, and developed a plain text problem format for evaluating LLM reasoning in this domain. We evaluated 7 LLMs (GPT-4o, GPT-4o-mini, o1, o1-mini, o3-mini, Claude-3.5 Sonnet, and Gemini-2.0-Flash), comparing 5 prompts to spur chain-of-thought reasoning in different ways, especially comparing the influence of providing background NMR chemistry knowledge, reasoning strategy, or both. Newer models trained to emphasize reasoning performed better, and increasing reasoning effort led to modest improvements, but prompting and varying temperature didn't have an effect. We also evaluated undergraduate organic chemistry students in a controlled setting, and analyzed answer submission statistics from global submissions to NMR-Challenge.com, to characterize human performance on these problems. The top-performing students surpassed smaller models like GPT-4o by 24%, 33%, and 29% on the Easy, Moderate, and Hard sets. However, reasoning models like o1 exceeded student performance by 13%, 14%, and 19%, respectively. Patterns in mistakes made by humans and LLMs reveal that errors made by LLMs are similar to those typically made by humans, for instance, incorrect positioning of substituents on benzene and incorrect orientation of carboxyl groups in esters. However, LLMs still "think" differently from humans, in some cases, providing answers which no human submitted via the website. This work also illustrates how NMR spectral problems can be used to benchmark LLMs on reasoning-heavy tasks in chemistry, though for this particular set of problems, current LLMs already exceed undergraduate student performance.
- Open Access
- 11 August 2025
- Published by Taylor & Francis in Molecular Physics
- Vol. 123 (21-22)
Benchmarking energy calculations using formal proofs
- 11 August 2025
- Published by Taylor & Francis in Molecular Physics
- Vol. 123 (21-22)
Open AccessBenchmarking energy calculations using formal proofs
- 10 July 2024
- Published by American Chemical Society (ACS) in Journal of Chemical Theory and Computation
- Vol. 20 (14) , 5854-5865
Monte Carlo Simulations of Water Pollutant Adsorption at Parts-per-Billion Concentration: A Study on 1,4-Dioxane
1,4-dioxane, an emerging water pollutant with high production volumes, is a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates the need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for the separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, and MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with a greater affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at a 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption and observe selectivities ranging from 1.1 x 10(5) in MOR to 8.7 x 10(6) in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in the aqueous phase at this concentration. This simulation technique can be extended to model other emerging water contaminants such as perfluoroalkyl and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.
- 10 July 2024
- Published by American Chemical Society (ACS) in Journal of Chemical Theory and Computation
- Vol. 20 (14) , 5854-5865
Monte Carlo Simulations of Water Pollutant Adsorption at Parts-per-Billion Concentration: A Study on 1,4-Dioxane
1,4-dioxane, an emerging water pollutant with high production volumes, is a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates the need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for the separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, and MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with a greater affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at a 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption and observe selectivities ranging from 1.1 x 10(5) in MOR to 8.7 x 10(6) in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in the aqueous phase at this concentration. This simulation technique can be extended to model other emerging water contaminants such as perfluoroalkyl and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.
- Open Access
- 1 June 2024
- Published by IOP Publishing in Machine Learning: Science and Technology
- Vol. 5 (2) , 025057
Incorporating background knowledge in symbolic regression using a computer algebra system
Symbolic regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.
- 1 June 2024
- Published by IOP Publishing in Machine Learning: Science and Technology
- Vol. 5 (2) , 025057
Open AccessIncorporating background knowledge in symbolic regression using a computer algebra system
Symbolic regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets. We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.
- Open Access
- 20 May 2024
- Published by American Chemical Society (ACS) in ChemRxiv
Monte Carlo simulations of water pollutant adsorption at parts-per-billion concentration: A study on 1,4-dioxane
1,4-dioxane is an emerging water pollutant with high production volumes and a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates a need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with more affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption, and observe selectivities ranging from 1.1 x 10^5 in MOR to 8.7 x 10^6 in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in both the aqueous and adsorbed phases at this concentration. This simulation technique can be extended to model other emerging water contaminants such as per- and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.
- 20 May 2024
- Published by American Chemical Society (ACS) in ChemRxiv
Open AccessMonte Carlo simulations of water pollutant adsorption at parts-per-billion concentration: A study on 1,4-dioxane
1,4-dioxane is an emerging water pollutant with high production volumes and a probable human carcinogen. The inadequacy of conventional treatment processes demonstrates a need for an effective remediation strategy. Crystalline nanoporous materials are cost-effective adsorbents due to their high capacity and selective separation in mixtures. This study explores the potential of all-silica zeolites for separation of 1,4-dioxane from water. These zeolites are highly hydrophobic and can preferentially adsorb nonpolar molecules from mixtures. We investigated six zeolite frameworks (BEA, EUO, FER, IFR, MFI, MOR) using Monte Carlo simulations in the Gibbs ensemble. The simulations indicate high selectivity by FER and EUO, especially at low pressures, which we attribute to pore sizes and shapes with more affinity to 1,4-dioxane. We also demonstrate a Monte Carlo simulation workflow using gauge cells to model the adsorption of an aqueous solution of 1,4-dioxane at 0.35 ppb concentration. We quantify 1,4-dioxane and water coadsorption, and observe selectivities ranging from 1.1 x 10^5 in MOR to 8.7 x 10^6 in FER. We also demonstrate that 1,4-dioxane is in the infinite dilution regime in both the aqueous and adsorbed phases at this concentration. This simulation technique can be extended to model other emerging water contaminants such as per- and polyfluoroalkyl substances (PFAS), chlorofluorocarbons, and others, which are also found in extremely low concentrations.
- Open Access
- 16 November 2023
- Published by Royal Society of Chemistry (RSC) in Digital Discovery
- Vol. 3 (2) , 264-280
Formalizing chemical physics using the Lean theorem prover
Theories in chemical physics can be reconstructed in a formal language using the interactive theorem prover, Lean. Lean’s ability to check math theorems catches faulty logic and reveals hidden assumptions that are missed in informal derivations.
- 16 November 2023
- Published by Royal Society of Chemistry (RSC) in Digital Discovery
- Vol. 3 (2) , 264-280
Open AccessFormalizing chemical physics using the Lean theorem prover
Theories in chemical physics can be reconstructed in a formal language using the interactive theorem prover, Lean. Lean’s ability to check math theorems catches faulty logic and reveals hidden assumptions that are missed in informal derivations.
- Open Access
- 12 April 2023
- Published by Springer Nature in Nature Communications
- Vol. 14 (1) , 1-10
Combining data and theory for derivable scientific discovery with AI-Descartes
Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem. We develop a method to enable principled derivations of models of natural phenomena from axiomatic knowledge and experimental data by combining logical reasoning with symbolic regression. We demonstrate these concepts for Kepler’s third law of planetary motion, Einstein’s relativistic time-dilation law, and Langmuir’s theory of adsorption. We show we can discover governing laws from few data points when logical reasoning is used to distinguish between candidate formulae having similar error on the data.
- 12 April 2023
- Published by Springer Nature in Nature Communications
- Vol. 14 (1) , 1-10
Open AccessCombining data and theory for derivable scientific discovery with AI-Descartes
Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general logical axioms is an open problem. We develop a method to enable principled derivations of models of natural phenomena from axiomatic knowledge and experimental data by combining logical reasoning with symbolic regression. We demonstrate these concepts for Kepler’s third law of planetary motion, Einstein’s relativistic time-dilation law, and Langmuir’s theory of adsorption. We show we can discover governing laws from few data points when logical reasoning is used to distinguish between candidate formulae having similar error on the data.