design of experiments by das and giri pdf

Academia.edu no longer supports Internet Explorer.

To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to  upgrade your browser .

Enter the email address you signed up with and we'll email you a reset link.

• We're Hiring!
• Help Center

Design and Analysis of Experiments. 8th Edition International Student Version

Related Papers

Ana Carolina Batosto Vargas

Preutipong Preutikun

Professor Mohamed Hassan Mehany H . Gadallah

Miguel Angel Ramos

Miraluna Herrera

Applied Stochastic Models in Business and Industry

Martín Tanco , Elisabeth Viles , María Alvarez

nonookok nonookoknonookok

Douglas C. Montgomery

Peter Goos , Bradley Jones

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED PAPERS

Critical Reviews in Therapeutic Drug Carrier Systems

manju dahiya

Handbook of Statistics

Russell Barton

Viatcheslav Melas

Naveen Ahuja

Fred J Hickernell

Quality and Reliability Engineering International

John Tyssedal

Journal of Complexity

Hans Visser , A. Beusen

Technometrics

roshan joseph

Journal of Pharmaceutical Innovation

Phillip Lunney , James Drennen

Mathematical Geology - MATH GEOL

Thomas Jones

Percy Soto Becerra

Aijun Zhang , Agus Sudjianto

IIE Transactions

Martín Tanco , Elisabeth Viles

2007 Winter Simulation Conference

Jack Kleijnen

Psychological Methods

Journal of the Italian Statistical Society

Renato Guseo

Fundamentals, Testing, and Processing Techniques

Mark Anderson , Patrick Whitcomb

Journal of Statistical Planning and Inference

Nam-Ky Nguyen

Mohammad Ahmadi

Aldi Wahyudi

Journal of Chromatography A

cristina maria silva

WATER (MDPI)

Fausto A Canales

Miller Puentes

Evelyng Taype Espinoza

Canadian Journal of Statistics

Judith Tanur

Nairanjana Dasgupta

•   We're Hiring!
•   Help Center
• Find new research papers in:
• Health Sciences
• Earth Sciences
• Cognitive Science
• Mathematics
• Computer Science
• Academia ©2024

Design and Analysis of Experiments

By m n das and narayan c giri.

• 2 Want to read
• 0 Currently reading
• 0 Have read

My Reading Lists:

Use this Work

Create a new list

My book notes.

My private notes about this edition:

Check nearby libraries

• Library.link

Buy this book

This edition doesn't have a description yet. Can you add one ?

Showing 1 featured edition. View all 1 editions?

Add another edition?

Book Details

Source records, community reviews (0).

• Created April 7, 2019

Wikipedia citation

Copy and paste this code into your Wikipedia page. Need help?

• General & Introductory Industrial Engineering

Design and Analysis of Experiments, 10th Edition

ISBN: 978-1-119-49244-3

Digital Evaluation Copy

Douglas C. Montgomery

Design and Analysis of Experiments provides a rigorous introduction to product and process design improvement through quality and performance optimization. Clear demonstration of widely practiced techniques and procedures allows readers to master fundamental concepts, develop design and analysis skills, and use experimental models and results in real-world applications. Detailed coverage of factorial and fractional factorial design, response surface techniques, regression analysis, biochemistry and biotechnology, single factor experiments, and other critical topics offer highly-relevant guidance through the complexities of the field.

Stressing the importance of both conceptual knowledge and practical skills, this text adopts a balanced approach to theory and application. Extensive discussion of modern software tools integrate data from real-world studies, while examples illustrate the efficacy of designed experiments across industry lines, from service and transactional organizations to heavy industry and biotechnology. Broad in scope yet deep in detail, this text is both an essential student resource and an invaluable reference for professionals in engineering, science, manufacturing, statistics, and business management.

• New Enhanced E-Text with added resources to make your study time more effective, including the ability to show/hide solutions for selected practice problems, helpful videos, supplemental text material linked from the e-text, and data sets linked from the e-text
• Revised and updated student problems are now presented at the beginning of chapters
• Selected problems have been reserved for instructor use
• Embedded links provide access to supplemental material, including new video content, study guide, and lecture slides
• Revised throughout for increased accuracy and up-to-date references
• Focuses on practical applications of widely-used software tools, including examples from Design-Expert, Minitab, JMP, and SAS
• Demonstrates how models are developed from experimental data
• Emphasizes the utility of experimental design to enhance product and process design, development, and optimization
• Covers all major design techniques, using a balanced approach to both design and analysis
• Presents multiple examples of both traditional and cutting-edge methods, providing foundational knowledge that translates directly to real-world skills

Ask the publishers to restore access to 500,000+ books.

Internet Archive Audio

• This Just In
• Grateful Dead
• Old Time Radio
• 78 RPMs and Cylinder Recordings
• Audio Books & Poetry
• Computers, Technology and Science
• Music, Arts & Culture
• News & Public Affairs
• Spirituality & Religion
• Radio News Archive

• Flickr Commons
• Occupy Wall Street Flickr
• NASA Images
• Solar System Collection
• Ames Research Center

• All Software
• Old School Emulation
• MS-DOS Games
• Historical Software
• Classic PC Games
• Software Library
• Kodi Archive and Support File
• Vintage Software
• CD-ROM Software
• CD-ROM Software Library
• Software Sites
• Tucows Software Library
• Shareware CD-ROMs
• Software Capsules Compilation
• CD-ROM Images
• ZX Spectrum
• DOOM Level CD

• Smithsonian Libraries
• FEDLINK (US)
• Lincoln Collection
• American Libraries
• Canadian Libraries
• Universal Library
• Project Gutenberg
• Children's Library
• Biodiversity Heritage Library
• Books by Language
• Additional Collections

• Prelinger Archives
• Democracy Now!
• Occupy Wall Street
• TV NSA Clip Library
• Animation & Cartoons
• Arts & Music
• Computers & Technology
• Cultural & Academic Films
• Ephemeral Films
• Sports Videos
• Videogame Videos
• Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

• Wayback Machine (iOS)
• Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

• Explore the Collections
• Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

• Donate Donate icon An illustration of a heart shape

Design and analysis of experiments

Bookreader item preview, share or embed this item, flag this item for.

• Graphic Violence
• Explicit Sexual Content
• Hate Speech
• Misinformation/Disinformation
• Marketing/Phishing/Advertising
• Misleading/Inaccurate/Missing Metadata

inherent skewed pages. some text runs to the top.

plus-circle Add Review comment Reviews

9 Favorites

DOWNLOAD OPTIONS

No suitable files to display here.

IN COLLECTIONS

Uploaded by station27.cebu on January 3, 2020

SIMILAR ITEMS (based on metadata)

• Science & Math
• Mathematics

Sorry, there was a problem.

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required .

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

Image Unavailable

• To view this video download Flash Player

Follow the author

Design and Analysis of Experiments Hardcover – December 31, 1979

• Language English
• Publisher John Wiley and Sons Ltd
• Publication date December 31, 1979
• ISBN-10 0852261586
• ISBN-13 978-0852261583
• See all details

Product details

• Publisher ‏ : ‎ John Wiley and Sons Ltd (December 31, 1979)
• Language ‏ : ‎ English
• ISBN-10 ‏ : ‎ 0852261586
• ISBN-13 ‏ : ‎ 978-0852261583

About the author

Discover more of the author’s books, see similar authors, read author blogs and more

Customer reviews

• 5 star 4 star 3 star 2 star 1 star 5 star 54% 32% 0% 14% 0% 54%
• 5 star 4 star 3 star 2 star 1 star 4 star 54% 32% 0% 14% 0% 32%
• 5 star 4 star 3 star 2 star 1 star 3 star 54% 32% 0% 14% 0% 0%
• 5 star 4 star 3 star 2 star 1 star 2 star 54% 32% 0% 14% 0% 14%
• 5 star 4 star 3 star 2 star 1 star 1 star 54% 32% 0% 14% 0% 0%

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

• Sort reviews by Top reviews Most recent Top reviews

Top reviews from the United States

Top reviews from other countries.

• About Amazon
• Investor Relations
• Amazon Devices
• Amazon Science
• Sell products on Amazon
• Sell on Amazon Business
• Sell apps on Amazon
• Become an Affiliate
• Advertise Your Products
• Self-Publish with Us
• Host an Amazon Hub
• › See More Make Money with Us
• Amazon Business Card
• Shop with Points
• Reload Your Balance
• Amazon Currency Converter
• Amazon and COVID-19
• Your Account
• Your Orders
• Shipping Rates & Policies
• Returns & Replacements
• Manage Your Content and Devices

• Conditions of Use
• Privacy Notice
• Consumer Health Data Privacy Disclosure
• Your Ads Privacy Choices

Pre-training with fractional denoising to enhance molecular property prediction

• Yuyan Ni   ORCID: orcid.org/0000-0002-8565-2627 1 , 2 , 3   na1   nAff6 ,
• Shikun Feng 1   na1 ,
• Xin Hong   ORCID: orcid.org/0000-0003-1524-9362 1 ,
• Yuancheng Sun 3 , 4 , 5 ,
• Wei-Ying Ma 1 ,
• Zhi-Ming Ma 2 , 3 ,
• Qiwei Ye 4 &
• Yanyan Lan   ORCID: orcid.org/0000-0002-7811-3262 1 , 5  

Nature Machine Intelligence ( 2024 ) Cite this article

Metrics details

• Computational chemistry
• Computational science
• Computer science
• Drug discovery
• Machine learning

A preprint version of the article is available at arXiv.

Deep learning methods have been considered promising for accelerating molecular screening in drug discovery and material design. Due to the limited availability of labelled data, various self-supervised molecular pre-training methods have been presented. Although many existing methods utilize common pre-training tasks in computer vision and natural language processing, they often overlook the fundamental physical principles governing molecules. In contrast, applying denoising in pre-training can be interpreted as an equivalent force learning, but the limited noise distribution introduces bias into the molecular distribution. To address this issue, we introduce a molecular pre-training framework called fractional denoising, which decouples noise design from the constraints imposed by force learning equivalence. In this way, the noise becomes customizable, allowing for incorporating chemical priors to substantially improve the molecular distribution modelling. Experiments demonstrate that our framework consistently outperforms existing methods, establishing state-of-the-art results across force prediction, quantum chemical properties and binding affinity tasks. The refined noise design enhances force accuracy and sampling coverage, which contribute to the creation of physically consistent molecular representations, ultimately leading to superior predictive performance.

This is a preview of subscription content, access via your institution

Access options

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

24,99 € / 30 days

cancel any time

Subscribe to this journal

Receive 12 digital issues and online access to articles

111,21 € per year

only 9,27 € per issue

Buy this article

• Purchase on SpringerLink
• Instant access to full article PDF

Prices may be subject to local taxes which are calculated during checkout

Data availability

The pre-training and fine-tuning data used in this work are available in the following links: PCQM4Mv2 (ref. 47 ), https://ogb.stanford.edu/docs/lsc/pcqm4mv2/ and https://figshare.com/articles/dataset/MOL_LMDB/24961485 (ref. 59 ); QM9 (refs. 42 , 43 ), https://figshare.com/collections/Quantum_chemistry_structures_and_properties_of_134_kilo_molecules/978904 (ref. 60 ); MD17 (ref. 35 ) and MD22 (ref. 37 ), http://www.sgdml.org/#datasets ; ISO17 (ref. 36 ), http://quantum-machine.org/datasets/ ; LBA 44 , https://zenodo.org/records/4914718 (ref. 61 ). Source data for the figures in this work are available via figshare at https://doi.org/10.6084/m9.figshare.25902679.v1 (ref. 62 ) and are provided with this paper.

Code availability

Source codes for Frad pre-training and fine-tuning are available via GitHub at https://github.com/fengshikun/FradNMI . The pre-trained models 63 are available via Zenodo at https://zenodo.org/records/12697467 (ref. 63 ).

Butler, K. T., Davies, D. W., Cartwright, H., Isayev, O. & Walsh, A. Machine learning for molecular and materials science. Nature 559 , 547–555 (2018).

Article   Google Scholar  

Wong, F. et al. Discovery of a structural class of antibiotics with explainable deep learning. Nature 626 , 177–185 (2023).

Li, J. et al. AI applications through the whole life cycle of material discovery. Matter 3 , 393–432 (2020).

Deng, J. et al. A systematic study of key elements underlying molecular property prediction. Nat. Commun. 14 , 6395 (2023).

Stokes, J. M. et al. A deep learning approach to antibiotic discovery. Cell 180 , 688–702 (2020).

Dowden, H. & Munro, J. Trends in clinical success rates and therapeutic focus. Nat. Rev. Drug Discov. 18 , 495–496 (2019).

Galson, S. et al. The failure to fail smartly. Nat. Rev. Drug Discov. 20 , 259–260 (2021).

Pyzer-Knapp, E. O. et al. Accelerating materials discovery using artificial intelligence, high performance computing and robotics. npj Comput. Mater. 8 , 84 (2022).

Schneider, G. Automating drug discovery. Nat. Rev. Drug Discov. 17 , 97–113 (2018).

Chen, T., Kornblith, S., Norouzi, M. & Hinton, G. A simple framework for contrastive learning of visual representations. In International Conference on Machine Learning 1597–1607 (PMLR, 2020).

He, K. et al. Masked autoencoders are scalable vision learners. In Proc. IEEE/CVF Conference on Computer Vision and Pattern Recognition 16000–16009 (IEEE, 2022).

Dai, A. M. & Le, Q. V. Semi-supervised sequence learning. Adv. Neural Inf. Process. Syst. 28 , 3079–3087 (2015).

Google Scholar  

Devlin, J., Chang, M.-W., Lee, K. & Toutanova, K. BERT: pre-training of deep bidirectional transformers for language understanding. In Proc. 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers) 4171–4186 (Association for Computational Linguistics, 2019).

Wang, Y., Wang, J., Cao, Z. & Barati Farimani, A. Molecular contrastive learning of representations via graph neural networks. Nat. Mach. Intell. 4 , 279–287 (2022).

Moon, K., Im, H.-J. & Kwon, S. 3D graph contrastive learning for molecular property prediction. Bioinformatics 39 , 371 (2023).

Fang, Y. et al. Knowledge graph-enhanced molecular contrastive learning with functional prompt. Nat. Mach. Intell . 5 , 542–553 (2023).

Stärk, H. et al. 3D Infomax improves GNNs for molecular property prediction. In International Conference on Machine Learning 20479–20502 (PMLR, 2022).

Liu, S. et al. Pre-training molecular graph representation with 3D geometry. In International Conference on Learning Representations Workshop on Geometrical and Topological Representation Learning https://openreview.net/pdf?id=xQUe1pOKPam (ICLR, 2022).

Li, S., Zhou, J., Xu, T., Dou, D. & Xiong, H. GeomGCL: geometric graph contrastive learning for molecular property prediction. In Proc. AAAI Conference on Artificial Intelligence 4541–4549 (PKP Publishing Services, 2022).

Zeng, X. et al. Accurate prediction of molecular properties and drug targets using a self-supervised image representation learning framework. Nat. Mach. Intell. 4 , 1004–1016 (2022).

Zhang, X.-C. et al. MG-BERT: leveraging unsupervised atomic representation learning for molecular property prediction. Brief. Bioinf. 22 , bbab152 (2021).

Ross, J. et al. Large-scale chemical language representations capture molecular structure and properties. Nat. Mach. Intell. 4 , 1256–1264 (2022).

Xia, J. et al. Mole-BERT: rethinking pre-training graph neural networks for molecules. In The Eleventh International Conference on Learning Representations https://openreview.net/pdf/21b1918178090348ffb159460ee696cfe8360dd2.pdf (ICLR, 2023).

Rong, Y. et al. Self-supervised graph transformer on large-scale molecular data. Adv. Neural Inf. Process. Syst. 33 , 12559–12571 (2020).

Fang, X. et al. Geometry-enhanced molecular representation learning for property prediction. Nat. Mach. Intell. 4 , 127–134 (2022).

Zhou, G. et al. Uni-Mol: a universal 3D molecular representation learning framework. In The Eleventh International Conference on Learning Representations https://openreview.net/pdf?id=IfFZr1gl0b (ICLR, 2023).

Wang, H. et al. Scientific discovery in the age of artificial intelligence. Nature 620 , 47–60 (2023).

Zaidi, S. et al. Pre-training via denoising for molecular property prediction. In International Conference on Learning Representations https://openreview.net/pdf?id=tYIMtogyee (ICLR, 2023).

Luo, S. et al. One transformer can understand both 2D & 3D molecular data. In The Eleventh International Conference on Learning Representations https://openreview.net/pdf?id=vZTp1oPV3PC (ICLR, 2023).

Liu, S., Guo, H. & Tang, J. Molecular geometry pretraining with SE(3)-invariant denoising distance matching. In The Eleventh International Conference on Learning Representations https://openreview.net/pdf?id=CjTHVo1dvR (ICLR, 2023).

Jiao, R., Han, J., Huang, W., Rong, Y. & Liu, Y. Energy-motivated equivariant pretraining for 3D molecular graphs. Proc. of the AAAI Conference on Artificial Intelligence 37 , 8096–8104 (2023).

Feng, R. et al. May the force be with you: unified force-centric pre-training for 3D molecular conformations. Adv. Neural Inf. Process. Syst. 36 , 72750–72760 (2023).

Thölke, P. & Fabritiis, G.D. Equivariant transformers for neural network based molecular potentials. In International Conference on Learning Representations https://openreview.net/pdf?id=zNHzqZ9wrRB (ICLR, 2022).

Boltzmann, L. Studien uber das gleichgewicht der lebenden kraft. Wissen. Abh. 1 , 49–96 (1868).

Chmiela, S. et al. Machine learning of accurate energy-conserving molecular force fields. Sci. Adv. 3 , 1603015 (2017).

Schütt, K. et al. SchNet: a continuous-filter convolutional neural network for modeling quantum interactions. Adv. Neural Inf. Process. Syst. 30 , 992–1002 (Curran Associates, 2017).

Chmiela, S. et al. Accurate global machine learning force fields for molecules with hundreds of atoms. Sci. Adv. 9 , 0873 (2023).

Chmiela, S., Sauceda, H. E., Müller, K.-R. & Tkatchenko, A. Towards exact molecular dynamics simulations with machine-learned force fields. Nat. Commun. 9 , 3887 (2018).

Wang, Y., Xu, C., Li, Z. & Barati Farimani, A. Denoise pretraining on nonequilibrium molecules for accurate and transferable neural potentials. J. Chem. Theory Comput. 19 , 5077–5087 (2023).

Smith, J. S., Isayev, O. & Roitberg, A. E. ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost. Chem. Sci. 8 , 3192–3203 (2017).

Smith, J. S. et al. The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules. Sci. Data 7 , 134 (2020).

Ruddigkeit, L., Van Deursen, R., Blum, L. C. & Reymond, J.-L. Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17. J. Chem. Inf. Model. 52 , 2864–2875 (2012).

Ramakrishnan, R., Dral, P. O., Rupp, M. & Von Lilienfeld, O. A. Quantum chemistry structures and properties of 134 kilo molecules. Sci. Data 1 , 140022 (2014).

Townshend, R. et al. ATOM3D: tasks on molecules in three dimensions. In Proc. Neural Information Processing Systems Track on Datasets and Benchmarks (2021).

Landrum, G. et al. RDKit: a software suite for cheminformatics, computational chemistry, and predictive modeling. Greg Landrum (2013).

Chmiela, S., Sauceda, H. E., Poltavsky, I., Müller, K.-R. & Tkatchenko, A. sGDML: constructing accurate and data efficient molecular force fields using machine learning. Comput. Phys. Commun. 240 , 38–45 (2019).

Nakata, M. & Shimazaki, T. PubChemQC project: a large-scale first-principles electronic structure database for data-driven chemistry. J. Chem. Inf. Model. 57 , 1300–1308 (2017).

Schütt, K. T., Sauceda, H. E., Kindermans, P.-J., Tkatchenko, A. & Müller, K.-R. SchNet—a deep learning architecture for molecules and materials. J. Chem. Phys. 148 , 241722 (2018).

Satorras, V. G., Hoogeboom, E. & Welling, M. E(n) equivariant graph neural networks. In International Conference on Machine Learning 9323–9332 (PMLR, 2021).

Gasteiger, J., Groß, J. & Günnemann, S. Directional message passing for molecular graphs. In International Conference on Learning Representations https://openreview.net/pdf?id=B1eWbxStPH (ICLR, 2020).

Gasteiger, J., Giri, S., Margraf, J.T. & Günnemann, S. Fast and uncertainty-aware directional message passing for non-equilibrium molecules. In Machine Learning for Molecules Workshop, NeurIPS (2020).

Liu, Y. et al. Spherical message passing for 3D molecular graphs. In International Conference on Learning Representations https://openreview.net/pdf?id=givsRXsOt9r (ICLR, 2022).

Schütt, K., Unke, O. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In International Conference on Machine Learning 9377–9388 (PMLR, 2021).

Öztürk, H., Özgür, A. & Ozkirimli, E. DeepDTA: deep drug–target binding affinity prediction. Bioinformatics 34 , 821–829 (2018).

Rao, R. et al. Evaluating protein transfer learning with tape. Adv. Neural Inf. Process. Syst. 32 , 9689–9701 (2019).

Elnaggar, A. et al. ProtTrans: toward understanding the language of life through self-supervised learning. IEEE Trans. Pattern Anal. Mach. Intell. 44 , 7112–7127 (2021).

Somnath, V. R., Bunne, C. & Krause, A. Multi-scale representation learning on proteins. Adv. Neural Inf. Process. Syst. 34 , 25244–25255 (2021).

Wang, L., Liu, H., Liu, Y., Kurtin, J. & Ji, S. Learning hierarchical protein representations via complete 3D graph networks. In The Eleventh International Conference on Learning Representations https://openreview.net/forum?id=9X-hgLDLYkQ (ICLR, 2022).

Feng, S. MOL_LMDB. figshare https://doi.org/10.6084/m9.figshare.24961485.v1 (2024).

Ramakrishnan, R., Dral, P., Rupp, M. & Anatole von Lilienfeld, O. Quantum chemistry structures and properties of 134 kilo molecules. figshare https://doi.org/10.6084/m9.figshare.c.978904.v5 (2014).

Townshend, R. J. L. ATOM3D: ligand binding affinity (LBA) dataset. Zenodo https://doi.org/10.5281/zenodo.4914718 (2021).

Ni, Y. Source data for figures in ‘Pre-training with fractional denoising to enhance molecular property prediction’. figshare https://doi.org/10.6084/m9.figshare.25902679.v1 (2024).

Feng, S. Pre-training with fractional denoising to enhance molecular property prediction. Zenodo https://doi.org/10.5281/zenodo.12697467 (2024).

Download references

Acknowledgements

Y.L. acknowledges funding from the National Key R&D Program of China (no. 2021YFF1201600) and the Beijing Academy of Artificial Intelligence (BAAI). We acknowledge B. Qiang, Y. Huang, C. Fan and H. Tang for valuable discussions.

Author information

Present address: Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China

These authors contributed equally: Yuyan Ni, Shikun Feng.

Authors and Affiliations

Institute for AI Industry Research (AIR), Tsinghua University, Beijing, China

Yuyan Ni, Shikun Feng, Xin Hong, Wei-Ying Ma & Yanyan Lan

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Yuyan Ni & Zhi-Ming Ma

University of Chinese Academy of Sciences, Beijing, China

Yuyan Ni, Yuancheng Sun & Zhi-Ming Ma

Institute of Automation, Chinese Academy of Sciences, Beijing, China

Yuancheng Sun & Qiwei Ye

Beijing Academy of Artificial Intelligence, Beijing, China

Yuancheng Sun & Yanyan Lan

You can also search for this author in PubMed   Google Scholar

Contributions

Y.N. and S.F. conceived the initial idea for the projects. S.F. processed the dataset and trained the model. Y.N. developed the theoretical results and drafted the initial manuscript. X.H. and Y.N. analysed the results and created the illustrations and data visualizations. S.F. and Y.S. carried out the experiments utilizing the pre-trained model. Y.N., S.F., X.H. and Y.L. participated in the revision of the paper. The project was supervised by Y.L., Q.Y., Z.-M.M. and W.-M.M., with funding obtained by Y.L. and Q.Y.

Corresponding author

Correspondence to Yanyan Lan .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Peer review

Peer review information.

Nature Machine Intelligence thanks Hosein Fooladi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended data fig. 1 test performance of coord and frad with different data accuracy on 3 tasks in qm9..

“Train from scratch" refers to the backbone model TorchMD-NET without pre-training. Both Coord and Frad use the TorchMD-NET backbone. “RDKit" and “DFT" refer to pre-training on molecular conformations generated by RDKit and DFT methods respectively. We can see that Frad is more robust to inaccurate pre-training conformations than Coord.

Source data

Extended data fig. 2 estimated force accuracy of frad and coord in three different sampling settings..

Force accuracy is measured by Pearson correlation coefficient ρ between the force estimation and ground truth. The estimation error is denoted as C e r r o r . We can see that within the range of small estimation errors, the force estimated by Frad( σ > 0) is consistently more accurate than that estimated by Coord( σ = 0).

Extended Data Fig. 3 Performance of Coord and Frad with different perturbation scales.

The performance (MAE) is averaged across seven energy prediction tasks in QM9. The perturbation scale refers to the mean absolute coordinate changes resulting from noise application and is determined by the noise scale. For Frad, the hyperparameter is fixed at τ = 0.04. We can see that Frad can effectively sample farther from the equilibrium, without a notable performance drop.

Extended Data Fig. 4 An illustration of model architecture.

The model primarily follows the TorchMD-NET framework, with our minor modifications highlighted in dotted orange boxes.

Supplementary information

Supplementary information.

Supplementary Notes A–E, Figs. 1 and 2 and Tables 1–15.

Source Data Fig. 2

Statistical source data.

Source Data Extended Data Fig./Table 1

Source data extended data fig./table 2, source data extended data fig./table 3, rights and permissions.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article.

Ni, Y., Feng, S., Hong, X. et al. Pre-training with fractional denoising to enhance molecular property prediction. Nat Mach Intell (2024). https://doi.org/10.1038/s42256-024-00900-z

Download citation

Received : 09 January 2024

Accepted : 15 August 2024

Published : 18 September 2024

DOI : https://doi.org/10.1038/s42256-024-00900-z

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: Translational Research newsletter — top stories in biotechnology, drug discovery and pharma.